Carter studies the influence of mechanical loading on the growth, development, regeneration, and aging of skeletal tissues. Basic information from these studies is used to understand skeletal diseases and treatments.

Academic Appointments

Administrative Appointments

  • Director of the Biomechanics and Mechanobiology Program BMMB/CMMI/ENG, National Science Foundation (2010 - 2014)

Professional Education

  • Ph.D., Stanford University, Biomedical Engineering (1976)
  • M.S.E., Stanford University, Bioengineering (1973)
  • B.S., University of Michigan, Aerospace Engineering (1971)

Research & Scholarship

Current Research and Scholarly Interests

Professor Carter studies the influence of mechanical loading upon the growth, development, regeneration, and aging of skeletal tissues. Basic information from such studies is used to understand skeletal diseases and treatments. He has served as President of the Orthopaedic Research Society and is a Fellow of the American Institute for Medical and Biological Engineering.


2014-15 Courses

Graduate and Fellowship Programs


Journal Articles

  • Improving the Estimate of the Effective Elastic Modulus Derived from Three-Point Bending Tests of Long Bones ANNALS OF BIOMEDICAL ENGINEERING Kourtis, L. C., Carter, D. R., Beaupre, G. S. 2014; 42 (8): 1773-1780


    Three-point bending tests are often used to determine the apparent or effective elastic modulus of long bones. The use of beam theory equations to interpret such tests can result in a substantial underestimation of the true effective modulus. In this study three-dimensional, nonlinear finite element analysis is used to quantify the errors inherent in beam theory and to create plots that can be used to correct the elastic modulus calculated from beam theory. Correction plots are generated for long bones representative of a variety of species commonly used in research studies. For a long bone with dimensions comparable to the mouse femur, the majority of the error in the effective elastic modulus results from deformations to the bone cross section that are not accounted for in the equations from beam theory. In some cases, the effective modulus calculated from beam theory can be less than one-third of the true effective modulus. Errors are larger: (1) for bones having short spans relative to bone length; (2) for bones with thin vs. thick cortices relative to periosteal diameter; and (3) when using a small radius or "knife-edge" geometry for the center loading ram and the outer supports in the three-point testing system. The use of these correction plots will enable researchers to compare results for long bones from different animal strains and to compare results obtained using testing systems that differ with regard to length between the outer supports and the radius used for the loading ram and outer supports.

    View details for DOI 10.1007/s10439-014-1027-3

    View details for Web of Science ID 000339399000017

    View details for PubMedID 24845868

  • Cartilage Nominal Strain Correlates With Shear Modulus and Glycosaminoglycans Content in Meniscectomized Joints JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME Song, Y., Carter, D. R., Giori, N. J. 2014; 136 (6)


    Postmeniscectomy osteoarthritis (OA) is hypothesized to be the consequence of abnormal mechanical conditions, but the relationship between postsurgical alterations in articular cartilage strain and in vivo biomechanical/biochemical changes in articular cartilage is unclear. We hypothesized that spatial variations in cartilage nominal strain (percentile thickness change) would correlate with previously reported in vivo articular cartilage property changes following meniscectomy. Cadevaric sheep knees were loaded in cyclic compression which was previously developed to mimic normal sheep gait, while a 4.7 T magnetic resonance imaging (MRI) imaged the whole joint. 3D cartilage strain maps were compared with in vivo sheep studies that described postmeniscectomy changes in shear modulus, phase lag, proteoglycan content and collagen organization/content in the articular cartilage. The area of articular cartilage experiencing high (overloaded) and low (underloaded) strain was significantly increased in the meniscectomized tibial compartment by 10% and 25%, respectively, while no significant changes were found in the nonmeniscectomized compartment. The overloaded and underloaded regions of articular cartilage in our in vitro specimens correlated with regions of in vivo shear modulus reduction. Glycosaminoglycans (GAG) content only increased at the underloaded articular cartilage but decreased at the overloaded articular cartilage. No significant correlation was found in phase lag and collagen organization/content changes with the strain variation. Comparisons between postsurgical nominal strain and in vivo cartilage property changes suggest that both overloading and underloading after meniscectomy may directly damage the cartilage matrix stiffness (shear modulus). Disruption of superficial cartilage by overloading might be responsible for the proteoglycan (GAG) loss in the early stage of postmeniscectomy OA.

    View details for DOI 10.1115/1.4027298

    View details for Web of Science ID 000335894800012

    View details for PubMedID 24671447

  • Physeal cartilage exhibits rapid consolidation and recovery in intact knees that are physiologically loaded JOURNAL OF BIOMECHANICS Song, Y., Lee, D., Shin, C. S., Carter, D. R., Giori, N. J. 2013; 46 (9): 1516-1523


    The growth plate (physis) is responsible for long bone growth through endochondral ossification, a process which can be mechanically modulated. However, our understanding of the detailed mechanical behavior of physeal cartilage occurring in vivo is limited. In this study, we aimed to quantify the time-dependent deformational behavior of physeal cartilage in intact knees under physiologically realistic dynamic loading, and compare physeal cartilage deformation with articular cartilage deformation. A 4.7 T MRI scanner continuously scanned a knee joint in the sagittal plane through the central load-bearing region of the medial compartment every 2.5 min while a realistic cyclic loading was applied. A custom auto-segmentation program was developed to delineate complex physeal cartilage boundaries. Physeal volume changes at each time step were calculated. The new auto-segmentation was found to be reproducible with COV of the volume measurements being less than 0.5%. Time-constants of physeal cartilage consolidation (1.31±0.74 min) and recovery (1.63±0.70 min) were significantly smaller than the values (5.53±1.78/17.71±13.88 min for consolidation/recovery) in articular cartilage (P<0.05). The rapid consolidation and recovery of physeal cartilage may due to a relatively free metaphyseal fluid boundary which would allow rapid fluid exchange with the adjacent cancellous bone. This may impair the generation of hydrostatic pressure in the cartilage matrix when the physis is under chronic compressive loading, and may be related to the premature ossification of the growth plate under such conditions. Research on the growth plate fluid exchange may provide a more comprehensive understanding of mechanisms and disorders of long bone growth.

    View details for DOI 10.1016/j.jbiomech2013.03.026

    View details for Web of Science ID 000320827700006

    View details for PubMedID 23608339

  • The low permeability of healthy meniscus and labrum limit articular cartilage consolidation and maintain fluid load support in the knee and hip JOURNAL OF BIOMECHANICS Haemer, J. M., Carter, D. R., Giori, N. J. 2012; 45 (8): 1450-1456


    The knee meniscus and hip labrum appear to be important for joint health, but the mechanisms by which these structures perform their functions are not fully understood. The fluid phase of articular cartilage provides compressive stiffness and aids in maintaining a low friction articulation. Healthy fibrocartilage, the tissue of meniscus and labrum, has a lower fluid permeability than articular cartilage. In this study we hypothesized that an important function of the knee meniscus and the hip labrum is to augment fluid retention in the articular cartilage of a mechanically loaded joint. Axisymmetric hyperporoelastic finite element models were analyzed for an idealized knee and an idealized hip. The results indicate that the meniscus maintained fluid pressure and inhibited fluid exudation in knee articular cartilage. Similar, but smaller, effects were seen with the labrum in the hip. Increasing the fibrocartilage permeability relative to that of articular cartilage gave a consolidation rate and loss of fluid load support comparable to that predicted by meniscectomy or labrectomy. The reduced articular cartilage fluid pressure that was calculated for the joint periphery is consistent with patterns of endochondral ossification and osteophyte formation in knee and hip osteoarthritis. High articular central strains and loss of fluid load support after meniscectomy could lead to fibrillation. An intact low-permeability fibrocartilage is important for limiting fluid exudation from articular cartilage in the hip and knee. This may be an important aspect of the role of fibrocartilage in protecting these joints from osteoarthritis.

    View details for DOI 10.1016/j.jbiomech.2012.02.015

    View details for Web of Science ID 000304216100017

    View details for PubMedID 22391467

  • Articular cartilage friction increases in hip joints after the removal of acetabular labrum JOURNAL OF BIOMECHANICS Song, Y., Ito, H., Kourtis, L., Safran, M. R., Carter, D. R., Giori, N. J. 2012; 45 (3): 524-530


    The acetabular labrum is believed to have a sealing function. However, a torn labrum may not effectively prevent joint fluid from escaping a compressed joint, resulting in impaired lubrication. We aimed to understand the role of the acetabular labrum in maintaining a low friction environment in the hip joint. We did this by measuring the resistance to rotation (RTR) of the hip, which reflects the friction of the articular cartilage surface, following focal and complete labrectomy. Five cadaveric hips without evidence of osteoarthritis and impingement were tested. We measured resistance to rotation of the hip joint during 0.5, 1, 2, and 3 times body weight (BW) cyclic loading in the intact hip, and after focal and complete labrectomy. Resistance to rotation, which reflects articular cartilage friction in an intact hip was significantly increased following focal labrectomy at 1-3 BW loading, and following complete labrectomy at all load levels. The acetabular labrum appears to maintain a low friction environment, possibly by sealing the joint from fluid exudation. Even focal labrectomy may result in increased joint friction, a condition that may be detrimental to articular cartilage and lead to osteoarthritis.

    View details for DOI 10.1016/j.jbiomech.2011.11.044

    View details for Web of Science ID 000300863600017

    View details for PubMedID 22176711

  • Changes in articular cartilage mechanics with meniscectomy: A novel image-based modeling approach and comparison to patterns of OA JOURNAL OF BIOMECHANICS Haemer, J. M., Song, Y., Carter, D. R., Giori, N. J. 2011; 44 (12): 2307-2312


    Meniscectomy is a significant risk factor for osteoarthritis, involving altered cell synthesis, central fibrillation, and peripheral osteophyte formation. Though changes in articular cartilage contact pressure are known, changes in tissue-level mechanical parameters within articular cartilage are not well understood. Recent imaging research has revealed the effects of meniscectomy on the time-dependent deformation of physiologically loaded articular cartilage. To determine tissue-level cartilage mechanics that underlie observed deformation, a novel finite element modeling approach using imaging data and a contacting indenter boundary condition was developed. The indenter method reproduces observed articular surface deformation and avoids assumptions about tangential stretching. Comparison of results from an indenter model with a traditional femur-tibia model verified the method, giving errors in displacement, solid and fluid stress, and strain below 1% (RMS) and 7% (max.) of the absolute maximum of the parameters of interest. Indenter finite element models using real joint image data showed increased fluid pressure, fluid exudation, loss of fluid load support, and increased tensile strains centrally on the tibial condyle after meniscectomy-patterns corresponding to clinical observations of cartilage matrix damage and fibrillation. Peripherally there was decreased consolidation, which corresponds to reduced contact and fluid pressure in this analysis. Clinically, these areas have exhibited advance of the subchondral growth front, biological destruction of the cartilage matrix, cartilage thinning, and eventual replacement of the cartilage via endochondral ossification. Characterizing the changes in cartilage mechanics with meniscectomy and correspondence with observed tissue-level effects may help elucidate the etiology of joint-level degradation seen in osteoarthritis.

    View details for DOI 10.1016/j.jbiomech.2011.04.014

    View details for Web of Science ID 000294033200019

    View details for PubMedID 21741046

  • Connective Tissue Growth Factor in Regulation of RhoA Mediated Cytoskeletal Tension Associated Osteogenesis of Mouse Adipose-Derived Stromal Cells PLOS ONE Xu, Y., Wagner, D. R., Bekerman, E., Chiou, M., James, A. W., Carter, D., Longaker, M. T. 2010; 5 (6)


    Cytoskeletal tension is an intracellular mechanism through which cells convert a mechanical signal into a biochemical response, including production of cytokines and activation of various signaling pathways.Adipose-derived stromal cells (ASCs) were allowed to spread into large cells by seeding them at a low-density (1,250 cells/cm(2)), which was observed to induce osteogenesis. Conversely, ASCs seeded at a high-density (25,000 cells/cm(2)) featured small cells that promoted adipogenesis. RhoA and actin filaments were altered by changes in cell size. Blocking actin polymerization by Cytochalasin D influenced cytoskeletal tension and differentiation of ASCs. To understand the potential regulatory mechanisms leading to actin cytoskeletal tension, cDNA microarray was performed on large and small ASCs. Connective tissue growth factor (CTGF) was identified as a major regulator of osteogenesis associated with RhoA mediated cytoskeletal tension. Subsequently, knock-down of CTGF by siRNA in ASCs inhibited this osteogenesis.We conclude that CTGF is important in the regulation of cytoskeletal tension mediated ASC osteogenic differentiation.

    View details for DOI 10.1371/journal.pone.0011279

    View details for Web of Science ID 000279135400023

    View details for PubMedID 20585662

  • Computational simulation of spontaneous bone straightening in growing children BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Carpenter, R. D., Carter, D. R. 2010; 9 (3): 317-328


    Periosteal surface pressures have been shown to inhibit bone formation and induce bone resorption, while tensile strains perpendicular to the periosteal surface have been shown to inhibit bone resorption and induce new bone deposition. A new computational model was developed to incorporate these experimental findings into simulations of spontaneous bone straightening in children with congenital posteromedial bowing of the tibia. Three-dimensional finite element models of the periosteum were used to determine the relationships between the defect angle and the distribution of bone surface pressures and strains due to growth-generated tensile strains in the periosteum. These relationships were incorporated into an iterative simulation to model development of a growing, bowed tibia with an initial defect angle of 27 degrees. When periosteal loads were included in the simulation, the defect angle decreased to 10 degrees after 2 years, and the bone straightened by an age of 25 years. When periosteal loads were not included in the simulation, the defect angle decreased to 23 degrees after 2 years, and a defect angle of 9 degrees remained at an age of 25 years. A "modeling drift" bone apposition/resorption pattern appeared only when periosteal loads were included. The results suggest that periosteal pressures and tensile strains induced by bone bowing can accelerate the process of bone straightening and lead to more complete correction of congenital bowing defects. Including the mechanobiological effects of periosteal surface loads in the simulations produced results similar to those seen clinically, with rapid straightening during the first few years of growth.

    View details for DOI 10.1007/s10237-009-0178-x

    View details for Web of Science ID 000277711400005

    View details for PubMedID 19921292

  • An approach to quantifying bone overloading and hypertrophy with applications to multiple experimental studies BONE Chen, J. C., Beaupre, G. S., Carter, D. R. 2010; 46 (2): 322-329


    Many studies have investigated mechanically induced bone formation in mice and rats by applying loads to the long bones, and measuring changes in periosteal cortical bone apposition rates. However, the results are difficult to compare among each other because the loading schemes are generally different. The purpose of the present study was to develop a theoretical framework for evaluating the mechanical stimulus based on the bone daily strain stimulus, which is a function of loading cycles and bone strains. The daily strain stimulus would act as a single unifying parameter for directly comparing data from existing in vivo experiments, and is applied here to twenty previous rat and mouse studies. To calculate the daily strain stimulus, we determined the periosteal daily strain stimulus necessary for bone maintenance (xi(peri,0)) and the strain-cycle weighting exponent (m). In the first approach, we applied data from Rubin and Lanyon's bone maintenance studies. We calculated xi(peri,0) to be 2793 microstrain/day, and m to be 4.5. In the second approach, we used Fritton et al. 's strain gage recordings to calculate xi(peri,0) to be 1496 microstrain/day, and used an m value of 11.88, equal to human bone compressive fatigue properties. Fatigue data provided physiological relevance, and was useful for applying an established remodeling theory to in vivo studies. For both approaches, xi(peri,0) was below the fracture level. We then analyzed the applied strains, cycles, and periosteal bone apposition rates from the previous studies. The range of daily strain stimuli calculated using the first approach was much larger than the range using the second approach (2793-17312 microstrain/day compared to 1496-7681 microstrain/day). None of the studies applied a daily strain stimulus above the complete fatigue failure level, but some studies applied loading that could result in major fatigue microdamage. Bone apposition rates generally increased with increasing daily strain stimulus, which was consistent with previous theoretical models. The results suggest that the daily strain stimulus may be a reasonable first approximation for predicting bone apposition rates in a consistent manner. The use of the daily strain stimulus may be helpful for improving the design of future bone loading studies.

    View details for DOI 10.1016/j.bone.2009.09.030

    View details for Web of Science ID 000274702800011

    View details for PubMedID 19800044

  • Biocompatibility of poly(ethylene glycol)/poly(acrylic acid) interpenetrating polymer network hydrogel particles in RAW 264.7 macrophage and MG-63 osteoblast cell lines. Journal of biomedical materials research. Part A Yim, E. S., Zhao, B., Myung, D., Kourtis, L. C., Frank, C. W., Carter, D., Smith, R. L., Goodman, S. B. 2009; 91 (3): 894-902


    Hydrogel polymers comprise a novel category of synthetic materials being investigated for use in cartilage replacement. One candidate compound, a poly(ethylene glycol)/poly(acrylic acid) (PEG/PAA) interpenetrating polymer network (IPN), was developed for use in corneal prostheses and was recently engineered for potential orthopedic use. The current study examined the effects of particles of this compound on two cell lines (MG-63 osteoblast-like cells and RAW 264.7 macrophages) over a 48-h time course. To mimic the effects of wear debris, particles of the compound were generated and introduced to the cells. In the MG-63 cell line, the particles had no significant effect on cell viability measured by PicoGreen assay and trypan blue exclusion. In contrast, a significant decrease in cell viability was detected in the Raw 264.7 macrophage cells at the final timepoint with the highest concentration of hydrogel (3.0% v:v). A concentration- and time-dependent increase in TNF-alpha release characteristic of other known biocompatible materials was also detected in RAW 264.7 cells, but nitric oxide and interleukin (IL)-1beta showed no response. In addition, the MG-63 cell line demonstrated no IL-6 response. Particles of the PEG/PAA IPN thus seem to stimulate biological responses similar to those in other biocompatible materials.

    View details for DOI 10.1002/jbm.a.32311

    View details for PubMedID 19072924

  • The pathogenesis of osteoarthritis in cerebral palsy DEVELOPMENTAL MEDICINE AND CHILD NEUROLOGY Carter, D. R., Tse, B. 2009; 51: 79-83


    The morphogenesis, remodeling, and degeneration of diarthroidial joints are directly under the control of the loading histories created by the musculoskeletal system during development and aging. The altered loading histories in individuals with cerebral palsy (CP) lead to aberrations in joint morphogenesis and an acceleration of joint degeneration. To understand this process in the hip, the normal ontogeny of the hip joint is reviewed with special attention to the mechano-biological factors associated with joint morphogenesis, endochondral ossification, and cartilage degeneration. A contrast is then made with the mechano-biological alterations observed with CP and the consequent influence on joint destruction. The features of the pathogenesis are: (1) altered muscular activity and restricted range of motion result in abnormal joint morphology, subluxation, and poor coverage of the femoral head; (2) joint incongruities created in early development cause local stress concentrations that can mechanically damage the articular cartilage; (3) the reduced magnitudes of muscular forces reduce the contact pressures at the joints, creating thinner cartilage and osteopenia; and (4) the thinner cartilage degenerates early, and subchondral bone collapse further contributes to the mechanical destruction of the remaining cartilage.

    View details for DOI 10.1111/j.1469-8749.2009.03435.x

    View details for Web of Science ID 000269539400011

    View details for PubMedID 19740213

  • The Periosteum as a Cellular Source for Functional Tissue Engineering TISSUE ENGINEERING PART A Arnsdorf, E. J., Jones, L. M., Carter, D. R., Jacobs, C. R. 2009; 15 (9): 2637-2642


    The periosteum, a specialized fibrous tissue composed of fibroblast, osteoblast, and progenitor cells, may be an optimal cell source for tissue engineering based on its accessibility, the ability of periosteal cells to proliferate rapidly both in vivo and in vitro, and the observed differentiation potential of these cells. However, the functional use of periosteum-derived cells as a source for tissue engineering requires an understanding of the ability of such cells to elaborate matrix of different tissues. In this study, we subjected a population of adherent primary periosteum-derived cells to both adipogenic and osteogenic culture conditions. The commitment propensity of periosteal cells was contrasted with that of well-characterized phenotypically pure populations of NIH3T3 fibroblast and MC3T3-E1 osteoblast cell lines. Our results demonstrate that the heterogeneous populations of periosteal cells and NIH3T3 fibroblasts have the ability to express both osteoblast-like and adipocyte-like markers with similar potential. This raises the question of whether fibroblasts within the periosteum may, in fact, have the potential to behave like progenitor cells and play a role in the tissue's multilineage potential or whether there are true stem cells within the periosteum. Further, this study suggests that expanded periosteal cultures may be a source for tissue engineering applications without extensive enrichment or sorting by molecular markers. Thus, this study lays the groundwork for future investigations that will more deeply enumerate the cellular sources and molecular events governing periosteal cell differentiation.

    View details for DOI 10.1089/ten.tea.2008.0244

    View details for Web of Science ID 000269221400029

    View details for PubMedID 19207046

  • Meniscectomy alters the dynamic deformational behavior and cumulative strain of tibial articular cartilage in knee joints subjected to cyclic loads OSTEOARTHRITIS AND CARTILAGE Song, Y., Greve, J. M., Carter, D. R., Giori, N. J. 2008; 16 (12): 1545-1554


    Meniscectomy-induced osteoarthritis may be mechanically based. We asked how meniscectomy alters time-dependent deformation of physiologically loaded articular cartilage. We hypothesized that meniscectomy alters nominal strain in tibial articular cartilage, and that meniscectomy affects cartilage thickness recovery following cessation of loading.A cyclic load simulating normal gait was applied to four sheep knees. A custom device was used to obtain MR images of cartilage at 4.7T during cyclic loading. Articular cartilage thickness and nominal strain were measured every 2.5 min during 1h of cyclic loading, and during 2.5h after cessation of loading.Following meniscectomy the loaded joints rapidly developed high strain centrally and minimal strain peripherally. Maximum nominal strains after 1h of loading were about 55% in the intact knees and 72% in the meniscectomized knees. Nominal strains in the peripheral tibial cartilage were significantly reduced in the meniscectomized knees. Strain recovery was markedly prolonged in the meniscectomized knees.With meniscectomy, tibial articular cartilage in the central load bearing region remains chronically deformed and dehydrated, even after cessation of loading. Post-meniscectomy osteoarthritis may be initiated in this region by direct damage to the cartilage matrix, or by altering the hydration of the tissue. In peripheral regions, reduced loading and strain may facilitate subchondral vascular invasion, and endochondral ossification. This is consistent with the central fibrillation and peripheral osteophyte formation seen in post-meniscectomy osteoarthritis.

    View details for DOI 10.1016/j.joca.2008.04.011

    View details for Web of Science ID 000261339700015

    View details for PubMedID 18514552

  • The mechanobiological effects of periosteal surface loads BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Carpenter, R. D., Carter, D. R. 2008; 7 (3): 227-242


    We have developed an improved mechanobiological model of bone morphogenesis and functional adaptation that includes the influences of periosteum tension and pressure on bone formation and resorption. Previous models assumed that periosteal and endosteal bone deposition and resorption rates are governed only by the local intracortical daily stress or strain stimulus caused by cyclic loading. The new model incorporates experimental findings that pressures on periosteal surfaces can impede bone formation or induce bone resorption, whereas periosteal tensile strains perpendicular to bone surfaces can impede bone resorption or induce bone formation. We propose that these effects can produce flattened or concave bone surfaces in regions of periosteal pressure and bone ridges in regions of periosteal tension. The model was implemented with computer simulations to illustrate the role of adjacent muscles on the development of the triangular cross-sectional geometry of the rat tibia. The results suggest that intracortical stresses dictate bone size, whereas periosteal pressures may work in combination with intracortical stresses and other mechanobiological factors in the development of local bone cross-sectional shapes.

    View details for DOI 10.1007/s10237-007-0087-9

    View details for Web of Science ID 000257103300006

    View details for PubMedID 17487517

  • Hydrostatic pressure enhances chondrogenic differentiation of human bone marrow stromal cells in osteochondrogenic medium ANNALS OF BIOMEDICAL ENGINEERING Wagner, D. R., Lindsey, D. P., Li, K. W., Tummala, P., Chandran, S. E., Smith, R. L., Longaker, M. T., Carter, D. R., Beaupre, G. S. 2008; 36 (5): 813-820


    This study demonstrated the chondrogenic effect of hydrostatic pressure on human bone marrow stromal cells (MSCs) cultured in a mixed medium containing osteogenic and chondrogenic factors. MSCs seeded in type I collagen sponges were exposed to 1 MPa of intermittent hydrostatic pressure at a frequency of 1 Hz for 4 h per day for 10 days, or remained in identical culture conditions but without exposure to pressure. Afterwards, we compared the proteoglycan content of loaded and control cell/scaffold constructs with Alcian blue staining. We also used real-time PCR to evaluate the change in mRNA expression of selected genes associated with chondrogenic and osteogenic differentiation (aggrecan, type I collagen, type II collagen, Runx2 (Cbfa-1), Sox9, and TGF-beta1). With the hydrostatic pressure loading regime, proteoglycan staining increased markedly. Correspondingly, the mRNA expression of chondrogenic genes such as aggrecan, type II collagen, and Sox9 increased significantly. We also saw a significant increase in the mRNA expression of type I collagen, but no change in the expression of Runx2 or TGF-beta1 mRNA. This study demonstrated that hydrostatic pressure enhanced differentiation of MSCs in the presence of multipotent differentiation factors in vitro, and suggests the critical role that this loading regime may play during cartilage development and regeneration in vivo.

    View details for DOI 10.1007/s10439-008-9448-5

    View details for Web of Science ID 000254755800013

    View details for PubMedID 18266109

  • Periosteal biaxial residual strains correlate with bone specific growth rates in chick embryos COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Chen, J. C., Zhao, B., Longaker, M. T., Helms, J. A., Carter, D. R. 2008; 11 (5): 453-461


    It has been proposed that periosteal residual tensile strains influence periosteal bone apposition and endochondral ossification. The role of bone growth rates on the development of residual strains is not well known. This study examined the relationships between specific growth rate and residual strains in chick tibiotarsi. We measured length and circumference during embryonic days 11-20 using microCT. Bones grew faster in length, with longitudinal and circumferential specific growth rates decreasing from 17 to 9% and 14 to 8% per day, respectively. To calculate residual strains, opening dimensions of incisions through the periosteum were analysed using finite element techniques. Results indicate that Poisson's ratio for an isotropic material model is between 0 and 0.04. For the model with Poisson's ratio 0.03, longitudinal and circumferential residual strains decreased from 46.2 to 29.3% and 10.6 to 3.9%, respectively, during embryonic days 14-20. Specific growth rates and residual strains were positively correlated (p<0.05).

    View details for DOI 10.1080/10255840802129817

    View details for Web of Science ID 000260457900004

    View details for PubMedID 18608339

  • A new software tool (VA-BATTS) to calculate bending, axial, torsional and transverse shear stresses within bone cross sections having inhomogeneous material properties COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Kourtis, L. C., Carter, D. R., Kesari, H., Beaupre, G. S. 2008; 11 (5): 463-476


    This study introduces, validates and demonstrates a new automated software tool (VA-BATTS) to calculate bone stresses within a bone cross section subjected to bending, axial, torsional and transverse shear far-field loading conditions, using quantitative computed tomography (QCT) data.A QCT image is imported and processed to generate a 2D finite element (FE) mesh of the bone with inhomogeneous (CT-based) transversely isotropic material properties. Bending and axial stresses are determined using inhomogeneous beam theory; torsional and transverse shear stresses are calculated using a new 2D FE formulation.Validation studies show excellent agreement between results obtained using VA-BATTS and results obtained using analytical 2D models and inhomogeneous 3D FE models.Out-of-plane bone stresses can be accurately calculated using a 2D analysis. Material inhomogeneity can have a marked effect on predicted stresses. In three-point bending experiments, transverse shear may present important contributions to the failure potential. The software is available at

    View details for DOI 10.1080/10255840801930728

    View details for Web of Science ID 000260457900005

    View details for PubMedID 19230145

  • Benefit of single-leaf resection for horizontal meniscus tear CLINICAL ORTHOPAEDICS AND RELATED RESEARCH Haemer, J. M., Wang, M. J., Carter, D. R., Giori, N. J. 2007: 194-202


    When treating a horizontal meniscus tear, the surgeon must decide whether to resect one or both leaves of the tear. We asked whether there is a biomechanical advantage to sparing one leaf when performing a partial meniscectomy for horizontal meniscus tear. We used pressure-sensitive film to measure the contact area, mean pressure, and peak pressure on the lateral tibial plateau of cadaveric sheep knees loaded to 2x body weight. For tears restricted to the posterior third, single-leaf resection decreased contact area by 40% compared with the intact case. Sparing one leaf was beneficial because resection of the second leaf reduced contact area an additional 15%. Similarly, mean pressure was increased 24% for single-leaf resection and an additional 27% for double-leaf resection. Peak pressure showed no differences with single- and double-leaf resections. For tears that span the entire meniscus, single-leaf resection reduced contact area by 59%, increased mean pressure by 55%, and increased peak pressure by 19%. Double-leaf resection in this situation did not change these values substantially, suggesting sparing one leaf offers no benefit over resecting both leaves with extensive horizontal meniscus tears.

    View details for DOI 10.1097/BLO.0b0I13e3180303b5c

    View details for Web of Science ID 000245575600030

    View details for PubMedID 17179782

  • Rapid growth of cartilage rudiments may generate perichondrial structures by mechanical induction BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Henderson, J. H., De la Fuente, L., Romero, D., Colnot, C. I., Huang, S., Carter, D. R., Helms, J. A. 2007; 6 (1-2): 127-137


    Experimental and theoretical research suggest that mechanical stimuli may play a role in morphogenesis. We investigated whether theoretically predicted patterns of stress and strain generated during the growth of a skeletal condensation are similar to in vivo expression patterns of chondrogenic and osteogenic genes. The analysis showed that predicted patterns of compressive hydrostatic stress (pressure) correspond to the expression patterns of chondrogenic genes, and predicted patterns of tensile strain correspond to the expression patterns of osteogenic genes. Furthermore, the results of iterative application of the analysis suggest that stresses and strains generated by the growing condensation could promote the formation and refinement of stiff tissue surrounding the condensation, a prediction that is in agreement with an observed increase in collagen bundling surrounding the cartilage condensation, as indicated by picro-sirius red staining. These results are consistent with mechanical stimuli playing an inductive or maintenance role in the developing cartilage and associated perichondrium and bone collar. This theoretical analysis provides insight into the potential importance of mechanical stimuli during the growth of skeletogenic condensations.

    View details for DOI 10.1007/s10237-006-0038-x

    View details for Web of Science ID 000243873500014

    View details for PubMedID 16691413

  • Gene regulation ex vivo within a wrap-around tendon TISSUE ENGINEERING Li, K. W., Lindsey, D. P., Wagner, D. R., Giori, N. J., Schurman, D. J., Goodman, S. B., Smith, R. L., Carter, D. R., Beaupre, G. S. 2006; 12 (9): 2611-2618


    This study tested the hypothesis that physiologic tendon loading modulates the fibrous connective tissue phenotype in undifferentiated skeletal cells. Type I collagen sponges containing human bone marrow stromal cells (MSCs) were implanted into the midsubstance of excised sheep patellar tendons. An ex vivo loading system was designed to cyclically stretch each tendon from 0 to 5% at 1.0 Hz. The MSC-sponge constructs were implanted into 2 tendon sites: the first site subjected to tension only and a second site located at an artificially created wrap-around region in which an additional compressive stress was generated transverse to the longitudinal axis of the tendon. The induced contact pressure at the wraparound site was 0.55 +/- 0.12 MPa, as quantified by pressure-sensitive film. An MSC-sponge construct was maintained free swelling in the same bath as an unloaded control. After 2 h of tendon stretching, the MSC-sponge constructs were harvested and real-time PCR was used to quantify Fos, Sox9, Cbfa1 (Runx2), and scleraxis mRNA expression as markers of skeletal differentiation. Two hours of mechanical loading distinctly altered MSC differentiation in the wrap-around region and the tensile-only region, as evidenced by differences in Fos and Sox9 mRNA expression. Expression of Fos mRNA was 13 and 52 times higher in the tensile-only and wrap-around regions, respectively, compared to the free-swelling controls. Expression of Sox9 mRNA was significantly higher (2.5-3 times) in MSCs from the wraparound region compared to those from the tensile-only region or in free-swelling controls. In contrast, expression levels for Cbfa1 did not differ among constructs. Scleraxis mRNA was not detected in any construct. This study demonstrates that the physiologic mechanical environment in the wrap-around regions of tendons provides stimuli for upregulating early response genes and transcription factors associated with chondrogenic differentiation. These differentiation responses begin within as little as 2 h after the onset of mechanical stimulation and may be the basis for the formation of fibrocartilage that is typically found in the wrap-around region of mature tendons in vivo.

    View details for Web of Science ID 000240780900021

    View details for PubMedID 16995794

  • Dose- and time-dependent effects of cyclic hydrostatic pressure on transforming growth factor-beta 3-induced chondrogenesis by adult human mesenchymal stem cells in vitro TISSUE ENGINEERING Miyanishi, K., Trindade, M. C., Lindsey, D. P., Beaupre, G. S., Carter, D. R., Goodman, S. B., Schurman, D. J., Smith, R. L. 2006; 12 (8): 2253-2262


    This study examined effects of varying magnitudes of intermittent hydrostatic pressure (IHP) applied for different times on chondrogenesis of adult human mesenchymal stem cells (hMSCs) in vitro. hMSCs were exposed to 0.1, 1, and 10 MPa of IHP at a frequency of 1 Hz for 4 h/day for 3, 7, and 14 days in the presence of transforming growth factor (TGF-beta3). Chondrogenesis was characterized by gene expression, macromolecule production, and extracellular matrix deposition. Exposure of hMSCs to 0.1 MPa of IHP increased SOX9 and aggrecan mRNA expression by 2.2- and 5.6-fold, respectively, whereas type II collagen mRNA expression responded maximally at 10 MPa. Production of sulfated glycosaminoglycan responded to IHP of 1 MPa and 10 MPa, whereas collagen levels increased only at 10 MPa. Morphologically, matrix condensation occurred with increased IHP, concomitant with collagen expression. This study demonstrated that different levels of IHP differentially modulate hMSC chondrogenesis in the presence of TGF-beta3. The data suggest that tissue engineering of articular cartilage through application or recruitment of hMSCs can be facilitated by mechanical stimulation.

    View details for Web of Science ID 000240345800019

    View details for PubMedID 16968165

  • Articular cartilage MR imaging and thickness mapping of a loaded knee joint before and after meniscectomy OSTEOARTHRITIS AND CARTILAGE Song, Y., Greve, J. M., Carter, D. R., Koo, S., Giori, N. J. 2006; 14 (8): 728-737


    We describe a technique to axially compress a sheep knee joint in an MRI scanner and measure articular cartilage deformation. As an initial application, tibial articular cartilage deformation patterns after 2 h of static loading before and after medial meniscectomy are compared.Precision was established for repeated scans and repeated segmentations. Accuracy was established by comparing to micro-CT measurements. Four sheep knees were then imaged unloaded, and while statically loaded for 2 h at 1.5 times body weight before and after medial meniscectomy. Images were obtained using a 3D gradient echo sequence in a 4.7 T MRI. Corresponding 3D cartilage thickness models were created. Nominal strain patterns for the intact and meniscectomized conditions were compared.Coefficients of variation were all 2% or less. Root mean squared errors of MR cartilage thickness measurements averaged less than 0.09 mm. Meniscectomy resulted in a 60% decrease in the contact area (P=0.001) and a 13% increase in maximum cartilage deformation (P=0.01). Following meniscectomy, there were greater areas of articular cartilage experiencing abnormally high and low nominal strains. Areas of moderate nominal strain were reduced.Medial meniscectomy resulted in increased medial tibial cartilage nominal strains centrally and decreased strains peripherally. Areas of abnormally high nominal strain following meniscectomy correlated with areas that are known to develop fibrillation and softening 16 weeks after medial meniscectomy. Areas of abnormally low nominal strain correlated with areas of osteophyte formation. Studies of articular cartilage deformation may prove useful in elucidating the mechanical etiology of osteoarthritis.

    View details for DOI 10.1016/j.joca.2006.01.011

    View details for Web of Science ID 000239386900002

    View details for PubMedID 16533610

  • Effects of hydrostatic pressure and transforming growth factor-beta 3 on adult human mesenchymal stem cell chondrogenesis in vitro TISSUE ENGINEERING Miyanishi, K., Trindade, M. C., Lindsey, D. P., Beaupre, G. S., Carter, D. R., Goodman, S. B., Schurman, D. J., Smith, R. L. 2006; 12 (6): 1419-1428


    This study examined the effects of intermittent hydrostatic pressure (IHP) and transforming growth factor-beta 3 on chondrogenesis of adult human mesenchymal stem cells (hMSCs) in vitro. Chondrogenic gene expression was determined by quantifying mRNA signal levels for SOX9, a transcription factor critical for cartilage development and the cartilage matrix proteins, aggrecan and type II collagen. Extracellular matrix production was determined by weight and histology. IHP was applied to hMSCs in pellet culture at a level of 10 MPa and a frequency of 1 Hz for 4 h per day for periods of 3, 7, and 14 days. hMSCs responded to addition of TGF-beta 3 (10 ng/mL) with a greater than 10-fold increase (p < 0.01) in mRNA levels for each, SOX9, type II collagen, and aggrecan during a 14-day culture period. Applying IHP in the presence of TGF-beta 3 further increased the mRNA levels for these proteins by 1.9-, 3.3-, and 1.6-fold, respectively, by day 14. Chondrogenic mRNA levels were increased with just exposure to IHP. Extracellular matrix deposition of type II collagen and aggrecan increased in the pellets as a function of treatment conditions and time of culture. This study demonstrated adjunctive effects of IHP on TGF-beta 3-induced chondrogenesis and suggests that mechanical loading can facilitate articular cartilage tissue engineering.

    View details for Web of Science ID 000239570400004

    View details for PubMedID 16846340

  • Relationships between tissue dilatation and differentiation in distraction osteogenesis MATRIX BIOLOGY Morgan, E. F., Longaker, M. T., Carter, D. R. 2006; 25 (2): 94-103


    Mechanical factors modulate the morphogenesis and regeneration of mesenchymally derived tissues via processes mediated by the extracellular matrix (ECM). In distraction osteogenesis, large volumes of new bone are created through discrete applications of tensile displacement across an osteotomy gap. Although many studies have characterized the matrix, cellular and molecular biology of distraction osteogenesis, little is known about relationships between these biological phenomena and the local physical cues generated by distraction. Accordingly, the goal of this study was to characterize the local physical environment created within the osteotomy gap during long bone distraction osteogenesis. Using a computational approach, we quantified spatial and temporal profiles of three previously identified mechanical stimuli for tissue differentiation-pressure, tensile strain and fluid flow-as well as another candidate stimulus-tissue dilatation (volumetric strain). Whereas pressure and fluid velocity throughout the regenerate decayed to less than 31% of initial values within 20 min following distraction, tissue dilatation increased with time, reaching steady state values as high as 43% strain. This dilatation created large reductions and large gradients in cell and ECM densities. When combined with previous findings regarding the effects of strain and of cell and ECM densities on cell migration, proliferation and differentiation, these results indicate two mechanisms by which tissue dilatation may be a key stimulus for bone regeneration: (1) stretching of cells and (2) altering cell and ECM densities. These results are used to suggest experiments that can provide a more mechanistic understanding of the role of tissue dilatation in bone regeneration.

    View details for DOI 10.1016/j.matbio.2005.10.006

    View details for Web of Science ID 000236135400005

    View details for PubMedID 16330195

  • Age-dependent properties and quasi-static strain in the rat sagittal suture JOURNAL OF BIOMECHANICS Henderson, J. H., Chang, L. Y., Song, H. M., Longaker, M. T., Carter, D. R. 2005; 38 (11): 2294-2301


    We measured the morphology of and performed tensile tests on sagittal sutures from rats of postnatal age 2 to 60 days. Using the properties measured ex vivo and a pressure vessel-based analysis, we estimated the quasi-static strain that had existed in the suture in vivo from 2 to 60 days. Sutural thickness, width, and stiffness per length were notable properties found to be age dependent. Sutural thickness increased 4.5-fold (0.11-0.50mm) between 2 and 60 days. Sutural width increased transiently between 2 and 20 days, peaking around 8 days; at 8 days, mean sutural width was 75% larger than mean sutural width at two days (0.35+/-0.07 (SD) vs. 0.20+/-0.06 mm). Sutural stiffness per length increased 4.4-fold (8.77-38.3N/mm/mm) between 2 and 60 days. The quasi-static sutural strain estimated to exist in vivo averaged 270+/-190 muepsilon between 2 and 60 days and was not age dependent. These findings provide data on the age-dependent sutural properties of infant to mature rats and provide the first estimate of quasi-static sutural strain in vivo in the rat. The findings show that during development the rat sagittal suture, as a structure, changes significantly and is exposed to quasi-static tensile strain in vivo due to intracranial pressure.

    View details for DOI 10.1016/j.jbiomech.2004.07.037

    View details for Web of Science ID 000232456400019

    View details for PubMedID 16154417

  • New QCT analysis approach shows the importance of fall orientation on femoral neck strength JOURNAL OF BONE AND MINERAL RESEARCH Carpenter, R. D., Beaupre, G. S., Lang, T. F., Orwoll, E. S., Carter, D. R. 2005; 20 (9): 1533-1542


    The influence of fall orientation on femur strength has important implications for understanding hip fracture risk. A new image analysis technique showed that the strength of the femoral neck in 37 males varied significantly along the neck axis and that bending strength varied by a factor of up to 2.8 for different loading directions.Osteoporosis is associated with decreased BMD and increased hip fracture risk, but it is unclear whether specific osteoporotic changes in the proximal femur lead to a more vulnerable overall structure. Nonhomogeneous beam theory, which is used to determine the mechanical response of composite structures to applied loads, can be used along with QCT to estimate the resistance of the femoral neck to axial forces and bending moments.The bending moment [My(theta)] sufficient to induce yielding within femoral neck sections was estimated for a range of bending orientations (theta) using in vivo QCT images of 37 male (mean age, 73 years; range, 65-87 years) femora. Volumetric BMD, axial stiffness, average moment at yield (M(y,avg)), maximum and minimum moment at yield (M(y,max) and M(y,min)), bone strength index (BSI), stress-strain index (SSI), and density-weighted moments of resistance (Rx and Ry) were also computed. Differences among the proximal, mid-, and distal neck regions were detected using ANOVA.My(theta) was found to vary by as much as a factor of 2.8 for different bending directions. Axial stiffness, M(y,avg), M(y,max), M(y,min), BSI, and Rx differed significantly between all femoral neck regions, with an overall trend of increasing axial stiffness and bending strength when moving from the proximal neck to the distal neck. Mean axial stiffness increased 62% between the proximal and distal neck, and mean M(y,avg) increased 53% between the proximal and distal neck.The results of this study show that femoral neck strength strongly depends on both fall orientation and location along the neck axis. Compressive yielding in the superior portion of the femoral neck is expected to initiate fracture in a fall to the side.

    View details for DOI 10.1359/JBMR.050510

    View details for Web of Science ID 000231490200005

    View details for PubMedID 16059625

  • Age-dependent residual tensile strains are present in the dura mater of rats JOURNAL OF THE ROYAL SOCIETY INTERFACE Henderson, J. H., Nacamuli, R. P., Zhao, B., Longaker, M. T., Carter, D. R. 2005; 2 (3): 159-167


    The objectives of this study were to determine whether residual tensile strains exist in the dura mater of mammals in vivo, and whether the strains are age-dependent. We made incisions in the parietal dura mater of immature and mature rats, and measured the retraction of the dura mater from each incision. We then used a finite-element model to calculate the strain present in the parietal dura mater of each rat. We found that age-dependent residual tensile strains are present in the dura mater of rats. The mean average residual strain of the immature rats was significantly larger than that of the mature rats (4.96+/-1.54% (s.d.) versus 0.39+/-0.13%, p<0.0001), with the mean strain calculated in the mature rats of the order of the minimum measurement that could be made using our experimental approach. In addition, in the immature rats mean residual strain in the longitudinal direction was significantly larger than mean residual strain in the transverse direction (6.11+/-3.62% versus 3.82+/-2.64%, p=0.0218). Our findings show that age-dependent residual tensile strains exist in the dura mater of rats. We speculate that these strains may reflect the rate and direction of cranial growth and may also influence cranial healing.

    View details for DOI 10.1098/rsif.2005.0035

    View details for Web of Science ID 000234341800004

    View details for PubMedID 16849176

  • Mechanobiology of mandibular distraction osteogenesis: finite element analyses with a rat model JOURNAL OF ORTHOPAEDIC RESEARCH Loboa, E. G., Fang, T. D., Parker, D. W., Warren, S. M., Fong, K. D., Longaker, M. T., Carter, D. R. 2005; 23 (3): 663-670


    Three-dimensional finite element (FE) analyses were performed to characterize the local mechanical environment created within the tissue regenerate during mandibular distraction osteogenesis (DO) in a rat model. Finite element models were created from three-dimensional computed tomography image data of rat hemi-mandibles at four different time points during an optimal distraction osteogenesis protocol (i.e., most successful protocol for bone formation): end latency (post-operative day (POD) 5), distraction day 2 (POD 7), distraction day 5 (POD 10), and distraction day 8 (POD 13). A 0.25 mm distraction was simulated and the resulting hydrostatic stresses and maximum principal tensile strains were determined within the tissue regenerate. When compared to previous histological findings, finite element analyses showed that tensile strains up to 13% corresponded to regions of new bone formation and regions of periosteal hydrostatic pressure with magnitudes less than 17 kPa corresponded to locations of cartilage formation. Tensile strains within the center of the gap were much higher, leading us to conclude that tissue damage would occur there if the tissue was not compliant enough to withstand such high strains, and that this damage would trigger formation of new mesenchymal tissue. These data were consistent with histological evidence showing mesenchymal tissue present in the center of the gap throughout distraction. Finite element analyses performed at different time points during distraction were instrumental in determining the changes in hydrostatic stress and tensile strain fields throughout distraction, providing a mechanical environment rationale for the different levels of bone formation in end latency, and distraction day 2, 5, and 8 specimens.

    View details for DOI 10.1016/j.orthres.2004.09.010

    View details for Web of Science ID 000229375000022

    View details for PubMedID 15885489

  • The mechanobiology of articular cartilage development and degeneration CLINICAL ORTHOPAEDICS AND RELATED RESEARCH Carter, D. R., Beaupre, G. S., Wong, M., Smith, R. L., Andriacchi, T. P., Schurman, D. J. 2004: S69-S77


    The development, maintenance, and destruction of cartilage are regulated by mechanical factors throughout life. Mechanical cues in the cartilage fetal endoskeleton influence the expression of genes that guide the processes of growth, vascular invasion, and ossification. Intermittent fluid pressure maintains the cartilage phenotype whereas mild tension (or shear) promotes growth and ossification. The articular cartilage thickness is determined by the position at which the subchondral growth front stabilizes. In mature joints, cartilage is thickest and healthiest where the contact pressure and cartilage fluid pressure are greatest. The depth-dependent histomorphology reflects the local fluid pressure, tensile strain, and fluid exudation. Osteoarthritis represents the final demise and loss of cartilage in the skeletal elements. The initiation and progression of osteoarthritis can follow many pathways and can be promoted by mechanical factors including: (1) reduced loading, which activates the subchondral growth front by reducing fluid pressure; (2) blunt impact, causing microdamage and activation of the subchondral growth front by local shear stress; (3) mechanical abnormalities that increase wear at the articulating surface; and (4) other mechanically related factors. Research should be directed at integrating our mechanical understanding of osteoarthritis pathogenesis and progression within the framework of cellular and molecular events throughout ontogeny.

    View details for DOI 10.1097/01.blo.0000144970.05107.7e

    View details for Web of Science ID 000224524400014

    View details for PubMedID 15480079

  • Pressure and shear differentially alter human articular chondrocyte metabolism - A review CLINICAL ORTHOPAEDICS AND RELATED RESEARCH Smith, R. L., Carter, D. R., Schurman, D. J. 2004: S89-S95


    Homeostasis of articular cartilage depends in part on mechanical loads generated during daily activity whereas inappropriate joint loads result in focal degeneration of cartilage, as occurs in osteoarthritis. We will review results of a series of questions regarding the effects of two types of mechanical loads-intermittent hydrostatic pressure and shear stress-on adult human articular chondrocytes in high-density monolayer culture. Intermittent hydrostatic pressure increased aggrecan and Type II collagen gene expression in normal chondrocytes and induced changes in the cell-associated proteins of normal and osteoarthritic chondrocytes. Hydrostatic pressure also counteracted inhibitory effects of bacterial lipopolysaccharide on matrix protein expression by cultured chondrocytes. Application of shear stress to osteoarthritic chondrocytes increased the release of the proinflammatory mediator, nitric oxide, decreased aggrecan and Type II collagen expression, and induced molecular changes associated with apoptosis whereas hydrostatic pressure increased matrix macromolecule expression. The findings show that the types of load comprising the mechanical loading environment of articular cartilage considerably alter chondrocyte metabolism and suggest that mechanical stimulation may be used for in vitro or in vivo approaches for cartilage engineering.

    View details for DOI 10.1097/01.blo.0000143938.30681.9d

    View details for Web of Science ID 000224524400016

    View details for PubMedID 15480081

  • A conical-collared intramedullary stem can improve stress transfer and limit micromotion CLINICAL BIOMECHANICS Mandell, J. A., Carter, D. R., Goodman, S. B., Schurman, D. J., Beaupre, G. S. 2004; 19 (7): 695-703


    The objective of this study was to quantify the effect of collar geometry on stress transfer and micromotion in idealized models of a cementless implant having an intramedullary stem.Intramedullary stems exist on several types of orthopaedic implants, including the femoral component of hip arthroplasties and segmental replacements used in the surgical treatment of a tumor or trauma in the diaphysis of a long bone.Using three-dimensional finite element analysis, we compared four idealized, straight-stemmed, axisymmetric prostheses: flat-collared (0 degrees), conical-collared (30 degrees and 60 degrees), and collarless tapered (80 degrees). We simulated axial and non-axial (20 degrees oblique) loads as well as non-ingrown and ingrown interface conditions.Without bone ingrowth, stress transfer to bone adjacent to the collar increased with collar angle. Micromotion at the distal stem increased moderately with collar angle from 0 degrees through 60 degrees, then increased markedly from 60 degrees to 80 degrees. With simulated bony ingrowth, the effect of the collar was greatly reduced.The results of this study suggest that the selection of collar angle represents a tradeoff between initial stress transfer and micromotion. Stems with conical collar angles in the range of 30-60 degrees can provide increased stress transfer compared to a flat collar design and reduced micromotion compared to a collarless tapered design.

    View details for DOI 10.1016/j.clinbiomech.2004.04.004

    View details for Web of Science ID 000223419500007

    View details for PubMedID 15288455

  • Mechanobiological predictions of growth front morphology in developmental hip dysplasia JOURNAL OF ORTHOPAEDIC RESEARCH Shefelbine, S. J., Carter, D. R. 2004; 22 (2): 346-352


    Developmental dysplasia of the hip (DDH) is the most common orthopedic problem of newborn children. Most clinicians and researchers agree that the primary cause of DDH is abnormal mechanical forces on the head of the femur due to limb position, pressure from the womb, or ligament laxity. The abnormal mechanical forces result in altered growth and bony deformities, in particular large neck-shaft and anteversion angles in the proximal femur and a shallow acetabulum. Previous studies have suggested that intermittent octahedral shear stress promotes growth and ossification, while intermittent hydrostatic compressive stress inhibits growth and ossification. We implemented these mechanobiological principles into a finite element model to predict the rate of progression of the growth front and the formation of coxa valga (large neck-shaft angle) in DDH. Under the assumed normal fetal loading conditions the hydrostatic stress was even across the growth front, but the octahedral shear stress was higher in the center than at the edges. This stress profile promoted growth in the center and a produced a convex growth front shape. Under loading conditions of the dysplastic hip, the octahedral shear stress was much larger on the medial side than on the lateral side, which promoted growth on the medial side and resulted in coxa valga. These results indicate that abnormal forces on the prenatal hip might influence total bone morphology and the development of DDH. These findings might help in understanding the etiology and pathology of other developmental bone deformities.

    View details for DOI 10.1016/j.orthres.2003.08.004

    View details for Web of Science ID 000220027800017

    View details for PubMedID 15013095

  • Mechanobiological predictions of femoral anteversion in cerebral palsy ANNALS OF BIOMEDICAL ENGINEERING Shefelbine, S. J., Carter, D. R. 2004; 32 (2): 297-305


    Many morphological changes occur during development of the proximal femur. The anteversion angle is a measure of the rotation of the neck of the femur around the diaphysis. In normal development anteversion is 30 degrees at birth and decreases to 15 degrees by skeletal maturity. In children with cerebral palsy (CP) anteversion often increases slightly and remains high throughout development. Previous models have proposed that cyclic hydrostatic stress decreases the growth rate while cyclic octahedral shear stress increases the growth rate. In this study we also examine changes in the growth direction caused by deformation of the developing cartilage. Using these mechanobiological principles we considered the influence of mechanical loads on the formation of the anteversion angle in normal and CP development. Loads were applied to a three-dimensional finite element model of the proximal femur. From the resulting stresses and deformations at the growth front we calculated the growth rate and growth direction and simulated the progression of the growth front over 6 months. The model predicted a decrease in anteversion angle (-2 degrees over 6 months) under normal-loading conditions, and an increase in anteversion (+ 1 degrees over 6 months) under CP-loading conditions. These results compare well with observations during skeletalgenesis, in which the anteversion angle decreases rapidly in the first few years of normal growth and may increase in children with CP.

    View details for Web of Science ID 000222464800012

    View details for PubMedID 15008378

  • Mechanobiology of mandibular distraction osteogenesis: experimental analyses with a rat model BONE Loboa, E. G., Fang, T. D., Warren, S. M., Lindsey, D. P., Fong, K. D., Longaker, M. T., Carter, D. R. 2004; 34 (2): 336-343


    We analyzed mechanobiological influences on successful distraction osteogenesis (DO). Mandibular distraction surgeries were performed on 15 adult male Sprague-Dawley rats. Animals underwent gradual distraction (GD), progressive lengthening by small increments (5-day latency followed by 0.25 mm distractions twice daily for 8 days followed by 28-day maturation period). Distracted hemimandibles were harvested on postoperative days (POD) 5, 7, 10, 13, and 41. Load-displacement curves were then recorded for ex vivo distractions of 0.25 mm and stresses determined. Histologically, new bone formation appeared in GD specimens on distraction day 2 (POD 7), filling 50-60% of the gap by distraction day 8 (POD 13), with nearly complete bony bridging at end maturation (POD 41). Average tensile strains imposed by each incremental distraction ranged from approximately 10% to 12.5% during distraction days 2-8 and were associated with bone apposition rates of about 260 microm/day. Because this GD protocol was previously determined to be optimal for DO, we conclude that strains within this range provide an excellent environment for de novo bone apposition. Distraction caused tissue damage in distraction day 2, 5, and 8 specimens as evidenced by distinct drops in the load/displacement curves. Taken together, our interpretation of these data is that daily distractions cause daily tissue damage which triggers new mesenchymal tissue formation.

    View details for DOI 10.1016/j.bone.2003.10.012

    View details for Web of Science ID 000220014000011

    View details for PubMedID 14962812

  • Sutural bone deposition rate and strain magnitude during cranial development BONE Henderson, J. H., Longaker, M. T., Carter, D. R. 2004; 34 (2): 271-280


    It is widely believed that rapid growth of the human brain generates tensile strain in cranial sutures, and that this strain influences the rate of bone deposition at the sutural margins during development. We developed general theoretical techniques for estimating sutural bone deposition rate and strain magnitude during mammalian cranial development. A geometry-based analysis was developed to estimate sutural bone deposition rate. A quasi-static stress analysis was developed to estimate sutural strain magnitude. We applied these techniques to the special case of normal cranial development in humans. The results of the bone deposition rate analysis indicate that average human sutural bone deposition rate is on the order of 100 microm/day at 1 month of age and decreases in an approximately exponential fashion during the first 4 years of life. The results of the strain analysis indicate that sutural strain magnitude is highly dependent on the assumed stiffness of the sutures, with estimated strain at 1 month of age ranging from approximately 20 to 400 microstrain. Regardless of the assumed stiffness of the sutures, the results indicate that sutural strain magnitude is small and decreases in an approximately exponential fashion during the first 4 years of life. The finding that both sutural bone deposition rate and strain magnitude decrease with increasing age is consistent with quasi-static tensile strain in sutures influencing sutural osteoblast activity in a dose-dependent manner. However, the small magnitude of the predicted strains suggests that tissue level strains in sutures may be too small to directly influence osteoblast biology. In light of these results, we suggest other biomechanical mechanisms, such as a tension-induced angiogenic environment in the sutures or mechanotransduction in the underlying dura mater, through which tension across sutures may regulate the rate of bone deposition in sutures.

    View details for DOI 10.1016/j.bone.2003.10.007

    View details for Web of Science ID 000220014000004

    View details for PubMedID 14962805

  • Mechanobiology of soft skeletal tissue differentiation-a computational approach of a fiber-reinforced poroelastic model based on homogeneous and isotropic simplifications BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Loboa, E. G., Wren, T. A., Beaupre, G. S., Carter, D. R. 2003; 2 (2): 83-96


    The material properties of multipotent mesenchymal tissue change dramatically during the differentiation process associated with skeletal regeneration. Using a mechanobiological tissue differentiation concept, and homogeneous and isotropic simplifications of a fiber-reinforced poroelastic model of soft skeletal tissues, we have developed a mathematical approach for describing time-dependent material property changes during the formation of cartilage, fibrocartilage, and fibrous tissue under various loading histories. In this approach, intermittently imposed fluid pressure and tensile strain regulate proteoglycan synthesis and collagen fibrillogenesis, assembly, cross-linking, and alignment to cause changes in tissue permeability (k), compressive aggregate modulus (H(A)), and tensile elastic modulus (E). In our isotropic model, k represents the permeability in the least permeable direction (perpendicular to the fibers) and E represents the tensile elastic modulus in the stiffest direction (parallel to the fibers). Cyclic fluid pressure causes an increase in proteoglycan synthesis, resulting in a decrease in k and increase in H(A) caused by the hydrophilic nature and large size of the aggregating proteoglycans. It further causes a slight increase in E owing to the stiffness added by newly synthesized type II collagen. Tensile strain increases the density, size, alignment, and cross-linking of collagen fibers thereby increasing E while also decreasing k as a result of an increased flow path length. The Poisson's ratio of the solid matrix, nu(s), is assumed to remain constant (near zero) for all soft tissues. Implementing a computer algorithm based on these concepts, we simulate progressive changes in material properties for differentiating tissues. Beginning with initial values of E=0.05 MPa, H(A)=0 MPa, and k=1 x 10(-13) m(4)/Ns for multipotent mesenchymal tissue, we predict final values of E=11 MPa, H(A)=1 MPa, and k=4.8 x 10(-15) m(4)/Ns for articular cartilage, E=339 MPa, H(A)=1 MPa, and k=9.5 x 10(-16) m(4)/Ns for fibrocartilage, and E=1,000 MPa, H(A)=0 MPa, and k=7.5 x 10(-16) m(4)/Ns for fibrous tissue. These final values are consistent with the values reported by other investigators and the time-dependent acquisition of these values is consistent with current knowledge of the differentiation process.

    View details for DOI 10.1007/s10237-003-0030-7

    View details for Web of Science ID 000208283100003

    View details for PubMedID 14586808

  • Mechanical strain affects dura mater biological processes: Implications for immature calvarial healing PLASTIC AND RECONSTRUCTIVE SURGERY Fong, K. D., Warren, S. M., Loboa, E. G., Henderson, J. H., Fang, T. D., Cowan, C. M., Carter, D. R., Longaker, M. T. 2003; 112 (5): 1312-1327


    The human brain grows rapidly during the first 2 years of life. This growth generates tensile strain in the overlying dura mater and neurocranium. Interestingly, it is largely during this 2-year growth period that infants are able to reossify calvarial defects. This clinical observation is important because it suggests that calvarial healing is most robust during the period of active intracranial volume expansion. With a rat model, it was previously demonstrated that immature dura mater proliferates more rapidly and produces more osteogenic cytokines and markers of osteoblast differentiation than does mature dura mater. It was therefore hypothesized that mechanical strain generated by the growing brain induces immature dura mater proliferation and increases osteogenic cytokine expression necessary for growth and healing of the overlying calvaria. Human and rat (n = 40) intracranial volume expansion was calculated as a function of age. These calculations demonstrated that 83 percent of human intracranial volume expansion is complete by 2 years of age and 90 percent of Sprague-Dawley rat intracranial volume expansion is achieved by 2 months of age. Next, the maximal daily circumferential tensile strains that could be generated in immature rat dura mater were calculated, and the corresponding daily biaxial tensile strains in the dura mater during this 2-month period were determined. With the use of a three-parameter monomolecular growth curve, it was calculated that rat dura mater experiences daily equibiaxial strains of at most 9.7 percent and 0.1 percent at birth (day 0) and 60 days of age, respectively. Because it was noted that immature dural cells may experience tensile strains as high as approximately 10 percent, neonatal rat dural cells were subjected to 10 percent equibiaxial strain in vitro, and dural cell proliferation and gene expression profiles were analyzed. When exposed to mechanical strain, immature dural cells rapidly proliferated (5.8-fold increase in proliferating cell nuclear antigen expression at 24 hours). Moreover, mechanical strain induced marked up-regulation of dural cell osteogenic cytokine production; transforming growth factor-beta1 messenger RNA levels increased 3.4-fold at 3 hours and fibroblast growth factor-2 protein levels increased 4.5-fold at 24 hours and 5.6-fold at 48 hours. Finally, mechanical strain increased dural cell expression of markers of osteoblast differentiation (2.8-fold increase in osteopontin levels at 3 hours). These findings suggest that mechanical strain can induce changes in dura mater biological processes and gene expression that may play important roles in coordinating the growth and healing of the neonatal calvaria.

    View details for DOI 10.1097/01.PRS.0000079860.14734.D6

    View details for Web of Science ID 000220062700014

    View details for PubMedID 14504515

  • Modelling cartilage mechanobiology PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES Carter, D. R., Wong, M. 2003; 358 (1437): 1461-1471


    The growth, maintenance and ossification of cartilage are fundamental to skeletal development and are regulated throughout life by the mechanical cues that are imposed by physical activities. Finite element computer analyses have been used to study the role of local tissue mechanics on endochondral ossification patterns, skeletal morphology and articular cartilage thickness distributions. Using single-phase continuum material representations of cartilage, the results have indicated that local intermittent hydrostatic pressure promotes cartilage maintenance. Cyclic tensile strains (or shear), however, promote cartilage growth and ossification. Because single-phase material models cannot capture fluid exudation in articular cartilage, poroelastic (or biphasic) solid/fluid models are often implemented to study joint mechanics. In the middle and deep layers of articular cartilage where poroelastic analyses predict little fluid exudation, the cartilage phenotype is maintained by cyclic fluid pressure (consistent with the single-phase theory). In superficial articular layers the chondrocytes are exposed to tangential tensile strain in addition to the high fluid pressure. Furthermore, there is fluid exudation and matrix consolidation, leading to cell 'flattening'. As a result, the superficial layer assumes an altered, more fibrous phenotype. These computer model predictions of cartilage mechanobiology are consistent with results of in vitro cell and tissue and molecular biology experiments.

    View details for DOI 10.1098/rstb.2003.1346

    View details for Web of Science ID 000185739500006

    View details for PubMedID 14561337

  • Articular cartilage functional histomorphology and mechanobiology: a research perspective BONE Wong, M., Carter, D. R. 2003; 33 (1): 1-13


    The histomorphogenesis of articular cartilage is regulated during skeletal development by the intermittent forces and motions imposed at diarthrodial joints. A key feature in this development is the formation of the superficial, transitional, radial, and calcified cartilage zones through the cartilage thickness. The histomorphological, biological, and mechanical characteristics of these zones can be correlated with the distributions of pressures, deformations, and pressure-induced fluid flow that are created in vivo. In a mature joint, cyclic loads produce cyclic hydrostatic fluid pressure through the entire cartilage thickness that is comparable in magnitude to the applied joint pressure. Prolonged physical activity can cause the total cartilage thickness to decrease about 5%, although the consolidation strains vary tremendously in the different zones. The superficial zone can experience significant fluid exudation and consolidation (compressive strains) in the range of 60% while the radial zone experiences relatively little fluid flow and consolidation. The topological variation in the histomorphologic appearance of articular cartilage is influenced by the local mechanical loading of chondrocytes in the different zones. Patterns of stress, strain, and fluid flow created in the joint result in spatial and temporal changes in the rates of synthesis and degradation of matrix proteins. When viewed over the course of a lifetime, even subtle difference in these cellular processes can affect the micro- and macro-morphology of articular cartilage. This hypothesis is supported by in vivo and ex vivo experiments where load-induced changes in matrix synthesis and catabolism, gene expression, and signal transduction pathways have been observed.

    View details for DOI 10.1016/S8756-3282(03)00083-8

    View details for Web of Science ID 000184879700001

    View details for PubMedID 12919695

  • Effects of creep and cyclic loading on the mechanical properties and failure of human achilles tendons ANNALS OF BIOMEDICAL ENGINEERING Wren, T. A., Lindsey, D. P., Beaupre, G. S., Carter, D. R. 2003; 31 (6): 710-717


    The Achilles tendon is one of the most frequently injured tendons in humans, and yet the mechanisms underlying its injury are not well understood. This study examines the ex vivo mechanical behavior of excised human Achilles tendons to elucidate the relationships between mechanical loading and Achilles tendon injury. Eighteen tendons underwent creep testing at constant stresses from 35 to 75 MPa. Another 25 tendons underwent sinusoidal cyclic loading at 1 Hz between a minimum stress of 10 MPa and maximum stresses of 30-80 MPa. For the creep specimens, there was no significant relationship between applied stress and time to failure, but time to failure decreased exponentially with increasing initial strain (strain when target stress is first reached) and decreasing failure strain. For the cyclically loaded specimens, secant modulus decreased and cyclic energy dissipation increased over time. Time and cycles to failure decreased exponentially with increasing applied stress, increasing initial strain (peak strain from first loading cycle), and decreasing failure strain. For both creep and cyclic loading, initial strain was the best predictor of time or cycles to failure, supporting the hypothesis that strain is the primary mechanical parameter governing tendon damage accumulation and injury. The cyclically loaded specimens failed faster than would be expected if only time-dependent damage occurred, suggesting that repetitive loading also contributes to Achilles tendon injuries.

    View details for DOI 10.1114/1.1569267

    View details for Web of Science ID 000183248400010

    View details for PubMedID 12797621

  • Scientific foundations - Equibiaxial tensile strain affects calvarial osteoblast biology JOURNAL OF CRANIOFACIAL SURGERY Fong, K. D., Nacamuli, R. P., Loboa, E. G., Henderson, J. H., Fang, T. D., Song, H. M., Cowan, C. M., Warren, S. M., Carter, D. R., Longaker, M. T. 2003; 14 (3): 348-355


    Mechanical tensile strain is believed to play an important role in regulating calvarial morphogenesis. To better understand the effects of mechanical strain on pathologic calvarial growth, we applied 10% constant equibiaxial tensile strain to neonatal rat calvarial osteoblast cultures and examined cellular proliferation, cytokine production, and extracellular matrix molecule expression. Mechanical strain markedly increased osteoblast proliferation as demonstrated by increased proliferating cell nuclear antigen (PCNA) protein. In addition, both transforming growth factor-beta1 (TGF-beta1) mRNA expression and fibroblast growth factor-2 (FGF-2) protein production were increased with exposure to strain. Moreover, mechanical strain induced expression of the extracellular matrix molecule collagen IalphaI. To further explore the relationship between mechanotransduction, osteogenesis, and angiogenesis, we examined the effect of mechanical strain on calvarial osteoblast expression of vascular endothelial growth factor (VEGF). Interestingly, we found that mechanical strain induced a rapid (within 3 hrs) increase in osteoblast VEGF expression. These data suggest that constant equibiaxial tensile strain-induced mechanotransduction can influence osteoblasts to assume an "osteogenic" and "angiogenic" phenotype, and these findings may have important implications for understanding the mechanisms of pathologic strain-induced calvarial growth.

    View details for Web of Science ID 000183221300013

  • Mechanical strain effects on dura mater biology: Implications for understanding immature calvarial healing CRANIOFACIAL SURGERY 10 Fong, K. D., Warren, S. M., Loboa, E. G., Henderson, J. H., Fang, T. D., Nacamuli, R. P., Carter, D. R., Longaker, M. T. 2003: 403-404
  • Temporal variations in mechanical stimuli during mandibular distraction osteogenesis CRANIOFACIAL SURGERY 10 Morgan, E. F., Loboa, E. G., Fang, T. D., Longaker, M. T., Carter, D. R. 2003: 447-449
  • Mechanical induction in limb morphogenesis: The role of growth-generated strains and pressures BONE Henderson, J. H., Carter, D. R. 2002; 31 (6): 645-653


    Morphogenesis is regulated by intrinsic factors within cells and by inductive signals transmitted through direct contact, diffusible molecules, and gap junctions. In addition, connected tissues growing at different rates necessarily generate complicated distributions of physical deformations (strains) and pressures. In this Perspective we present the hypothesis that growth-generated strains and pressures in developing tissues regulate morphogenesis throughout development. We propose that these local mechanical cues influence morphogenesis by: (1) modulating growth rates; (2) modulating tissue differentiation; (3) influencing the direction of growth; and (4) deforming tissues. It is in this context that we review concepts and experiments of cell signaling and gene expression in various mechanical environments. Tissue and organ culture experiments are interpreted in light of the developmental events associated with the growth of the limb buds and provide initial support for the presence and morphological importance of growth-generated strains and pressures. The concepts presented are used to suggest future lines of research that may give rise to a more integrated mechanobiological view of early embryonic musculoskeletal morphogenesis.

    View details for Web of Science ID 000180111300002

    View details for PubMedID 12531557

  • Development of the femoral bicondylar angle in hominid bipedalism BONE Shefelbine, S. J., Tardieu, C., Carter, D. R. 2002; 30 (5): 765-770


    The bicondylar angle is the angle between the diaphysis of the femur and a line perpendicular to the infracondylar plane. The presence of a femoral bicondylar angle in Australopithecus afarensis indicates that these 3.5-million-year-old hominids were bipedal. Many studies have linked the formation of the femoral bicondylar angle with bipedality, but the mechanism for the formation of the angle is poorly understood. Mechanical factors, such as stresses and strains, influence the growth process. In particular, previous studies have demonstrated that hydrostatic compressive stress inhibits growth and ossification, and octahedral shear stress promotes growth and ossification. In this study we implemented these mechanobiological principles in a three-dimensional finite-element model of the distal femur. We applied loading conditions to the model to simulate loading during the single-leg stance phase of bipedal gait. The stresses in the physis of the distal femur that result from bipedal loading conditions promote growth and ossification more on the medial side than on the lateral side of the femur, forming the bicondylar angle. This model explains the presence of the bicondylar angle in hominid bipedalism and also the ontogenetic development of the bicondylar angle in growing children. The mechanobiological relationship between endochondral ossification and mechanical loading provides valuable insight into bone development and morphology.

    View details for Web of Science ID 000175804300017

    View details for PubMedID 11996917

  • Mechanical evaluation of a carbonated apatite cement in the fixation of unstable intertrochanteric fractures ACTA ORTHOPAEDICA SCANDINAVICA Yetkinler, D. N., Goodman, S. B., Reindel, E. S., Carter, D., Poser, R. D., Constantz, B. R. 2002; 73 (2): 157-164


    We created three-part unstable intertrochanteric fractures in 6 pairs of aged, osteopenic, human, cadaveric femora. Fractures were reduced and fixed with a Dynamic Hip Screw (DHS) (Synthes, Paoli, PA). Two test groups were evaluated: 1. Fixation with DHS, and 2. Fixation with a DHS and calcium phosphate bone cement (Norian SRS (Skeletal Repair System)) augmentation of the fracture line and posteromedial calcar region of the proximal femur. Each femur was loaded to 1,650 N (2.5 body weight) for 10,000 cycles to simulate postoperative load transmission across the fracture construct during normal gait. The load was further increased successively by one body weight for another 10,000 cycles until failure. We evaluated fixation by measuring the amount of sliding of the lag screw of the DHS (shortening) and stiffness of the overall fracture construct (stability). SRS cement-augmented specimens had less shortening (1 mm versus 17 mm) and twice the initial construct stiffness compared to control specimens.

    View details for Web of Science ID 000175929300007

    View details for PubMedID 12079012

  • Failure and fatigue characteristics of adhesive athletic tape MEDICINE AND SCIENCE IN SPORTS AND EXERCISE Bragg, R. W., MacMahon, J. M., Overom, E. K., Yerby, S. A., Matheson, G. O., Carter, D. R., Andriacchi, T. P. 2002; 34 (3): 403-410


    Athletic tape has been commonly reported to lose much of its structural support after 20 min of exercise. Although many studies have addressed the functional performance characteristics of athletic tape, its mechanical properties are poorly understood. This study examines the failure and fatigue properties of several commonly used athletic tapes.A Web-based survey of professional sports trainers was used to select the following three tapes for the study: Zonas (Johnson & Johnson), Leukotape (Beiersdorf), and Jaylastic (Jaybird & Mais). Using a hydraulic material testing system (MTS), eight samples of each tape were compared in three different mechanical tests: load-to-failure, fatigue testing under load control, and fatigue testing under displacement control. Differences in tape microstructure were used to interpret the results of the mechanical tests.Significant differences (P < 0.001) in failure load, elongation at failure, and stiffness were found from failure tests. Significant differences were also found (P < 0.001) in fatigue behavior under both modes of control. As a representative example, in one normalized displacement control fatigue test after 20 min of cycling, 21% (Zonas), 29% (Leukotape), and 57% (Jaylastic) of the mechanical support was lost. After cycling, all tapes loaded to failure showed increased stiffness (P < 0.001), indicating significant energy absorption during cycling. Observed differences in the tapes' microstructure were qualitatively consistent with the measured differences in their mechanical properties.In understanding the shortcomings of currently available tapes, the results of these tests can now be used as benchmarks with which to compare and develop future tape designs. Ultimately, these improved tapes should reduce ankle injuries among athletes.

    View details for Web of Science ID 000174268300004

    View details for PubMedID 11880802

  • A theoretical analysis of the contributions of remodeling space, mineralization, and bone balance to changes in bone mineral density during alendronate treatment BONE Hernandez, C. J., Beaupre, G. S., Marcus, R., Carter, D. R. 2001; 29 (6): 511-516


    In patients with osteoporosis, alendronate treatment causes an increase in bone mineral density (BMD) and a decrease in fracture incidence. Alendronate acts by changing the bone remodeling process. Changes in bone remodeling resulting in decreased remodeling space, increased bone balance per remodeling cycle, and increased mineralization (ash mass/bone mass) have all been associated with alendronate treatment. Understanding the relative contributions of these parameters to BMD increases could help predict the utility of long-term (>10 years) or intermittent treatment strategies, as well as treatment strategies in which another pharmaceutical is administered concurrently. We have developed a computer simulation of bone remodeling to compare the contributions of focal bone balance and mineralization on BMD by simulating alendronate treatment using a bone balance method (decreased remodeling space, increased focal bone balance, uniform bone mineralization) and a mineralization method (decreased remodeling space, neutral focal bone balance, varying bone mineralization). Although both methods are able to predict BMD increases caused by alendronate over short periods, our findings suggest that the mineralization method may be more descriptive of long-term alendronate treatment. This implies that mineralization may be a larger contributor to BMD changes caused by alendronate than the focal bone balance. Based on this finding we offer a hypothesis to describe how remodeling space, focal bone balance, and mineralization each contribute to alendronate-induced BMD changes. Future analyses with this method could be used to identify improved dosing regimens and to predict which osteoporosis treatments would best complement each other.

    View details for Web of Science ID 000172737500004

    View details for PubMedID 11728920

  • Mechanobiology of initial pseudarthrosis formation with oblique fractures JOURNAL OF ORTHOPAEDIC RESEARCH Loboa, E. G., Beaupre, G. S., Carter, D. R. 2001; 19 (6): 1067-1072


    Mechanical stresses play an important role in regulating tissue differentiation in a variety of contexts during skeletal development and regeneration. It has been shown that some intermittent loading at a fracture site can accelerate secondary fracture healing. However, it has not been shown how the stress and strain histories resulting from mechanical loading of a fracture might, in some cases, inhibit normal fracture healing and induce pseudarthrosis formation. In this study, finite element analysis is used to calculate hydrostatic stress and maximum principal tensile strain patterns in regenerating tissue around the site of an oblique fracture. Using a mechanobiologic view on tissue differentiation, we compared calculated stress and strain patterns within the fracture callus to the histomorphology of a typical oblique pseudarthrosis. Tissue differentiation predictions were consistent with the characteristic histomorphology of oblique pseudarthrosis: in the interfragmentary gap. tensile strains led to "cleavage" of the callus; at the ends of both fracture fragments, hydrostatic pressure and tensile strain caused fibrocartilage formation, and, at discrete locations of the periosteum at the oblique fracture ends, mild hydrostatic tension caused bone formation. We also found that discrete regions of high hydrostatic pressure correlated with locations of periosteal bone resorption. When previous findings with distraction osteogenesis are considered with these observations, it appears that low levels of hydrostatic pressure may be conducive to periosteal cartilage formation but high hydrostatic pressure may induce periosteal bone resorption during bone healing. We concluded that tissue differentiation in pseudarthrosis formation is consistent with concepts previously presented for understanding fracture healing, distraction osteogenesis, and joint formation.

    View details for Web of Science ID 000172916000011

    View details for PubMedID 11781006

  • The influence of bone volume fraction and ash fraction on bone strength and modulus BONE Hernandez, C. J., Beaupre, G. S., Keller, T. S., Carter, D. R. 2001; 29 (1): 74-78


    Although bone strength and modulus are known to be influenced by both volume fraction and mineral content (ash fraction), the relative influence of these two parameters remains unknown. Single-parameter power law functions are used widely to relate bone volume or ash fraction to bone strength and elastic modulus. In this study we evaluate the potential for predicting bone mechanical properties with two-parameter power law functions of bone volume fraction (BV/TV) and ash fraction (alpha) of the form y = a(BV/TV)(b) alpha(c) (where y is either ultimate strength or elastic modulus). We derived an expression for bone volume fraction as a function of apparent density and ash fraction to perform a new analysis of data presented by Keller in 1994. Exponents b and c for the prediction of bone strength were found to be 1.92 +/- 0.02 and 2.79 +/- 0.09 (mean +/- SE), respectively, with r(2) = 0.97. The value of b was found to be consistent with that found previously, whereas the value of c was lower than values previously reported. For the prediction of elastic modulus we found b and c to be 2.58 +/- 0.02 and 2.74 +/- 0.13, respectively, with r(2) = 0.97. The exponent related to ash fraction was typically larger than that associated with bone volume fraction, suggesting that a change in mineral content will, in general, generate a larger change in bone strength and stiffness than a similar change in bone volume fraction. These findings are important for interpreting the results of antiresorptive drug treatments that can cause changes in both ash and bone volume fraction.

    View details for Web of Science ID 000170219400011

    View details for PubMedID 11472894

  • Influence of bone mineral density, age, and strain rate on the failure mode of human Achilles tendons CLINICAL BIOMECHANICS Wren, T. A., Yerby, S. A., Beaupre, G. S., Carter, D. R. 2001; 16 (6): 529-534


    To examine the influence of strain rate, bone mineral density, and age in determining the mode by which human Achilles tendons fail.Dual-energy X-ray absorptiometry and mechanical testing of excised Achilles tendon-calcaneus specimens.The Achilles tendon can fail by tendon rupture or bony avulsion. These injuries are caused by similar loading mechanisms and can present similar symptoms. It is important to understand when each mode of injury is likely to occur so that accurate diagnoses can be made and appropriate treatments selected.Excised human Achilles tendons were loaded to failure at strain rates of 1% s(-1) and 10% s(-1) following dual-energy X-ray absorptiometry examination to determine bone mineral density near the tendon insertion. Calcaneal bone mineral density, donor age, and strain rate were compared between specimens that failed by avulsion and those that failed by tendon rupture.While strain rate was not observed to affect failure mode, the calcaneal bone mineral density of specimens that failed by avulsion was significantly lower than the bone mineral density of specimens that failed by tendon rupture (P=0.004). There was a significant decrease in bone mineral density with age (P=0.004), and the difference in age between the avulsed and ruptured specimens was close to statistical significance (P=0.058). For the avulsed specimens, there was a significant linear relationship between failure load and bone mineral density squared (P=0.002). Logistic regression indicated that the effect of age on failure mode is secondary to the primary effect of bone mineral density.The avulsions were primarily "premature" failures associated with low bone mineral density. Since bone mineral density decreases with age, older individuals are more likely to experience avulsions while younger individuals are more likely to experience tendon ruptures.

    View details for Web of Science ID 000170279500009

    View details for PubMedID 11427296

  • Mechanical properties of the human Achilles tendon CLINICAL BIOMECHANICS Wren, T. A., Yerby, S. A., Beaupre, G. S., Carter, D. R. 2001; 16 (3): 245-251


    To determine whether the human Achilles tendon has higher material properties than other tendons and to test for strain rate sensitivity of the tendon.Mechanical testing of excised tendons.While the human Achilles tendon appears to experience higher in vivo stresses than other tendons, it is not known how the Achilles tendon's material properties compare with the properties of other tendons.Modulus, failure stress, and failure strain were measured for excised human Achilles tendons loaded at strain rates of 1% s(-1) and 10% s(-1). Paired t-tests were used to examine strain rate effects, and average properties from grouped data were used to compare the Achilles tendon's properties with properties reported in the literature for other tendons.Failure stress and failure strain were higher at the faster strain rate, but no significant difference in modulus was observed. At the 1% s(-1)rate, the mean modulus and failure stress were 816 MPa (SD, 218) and 71 MPa (SD, 17), respectively. The failure strain was 12.8% (SD, 1.7) for the bone-tendon complex and 7.5% (SD, 1.1) for the tendon substance. At the 10% s(-1) rate, the mean modulus and failure stress were 822 MPa (SD, 211) and 86 MPa (SD, 24), respectively. The mean failure strain was 16.1% (SD, 3.6) for the bone-tendon complex and 9.9% (SD, 1.9) for the tendon substance. These properties fall within the range of properties reported in the literature for other tendons.The material properties of the human Achilles tendon measured in this study are similar to the properties of other tendons reported in the literature despite higher stresses imposed on the Achilles tendon in vivo.

    View details for Web of Science ID 000167502300010

    View details for PubMedID 11240060

  • Biomechanical comparison of conventional open reduction and internal fixation versus calcium phosphate cement fixation of a central depressed tibial plateau fracture JOURNAL OF ORTHOPAEDIC TRAUMA Yetkinler, D. N., McClellan, R. T., Reindel, E. S., Carter, D., Poser, R. D. 2001; 15 (3): 197-206


    To evaluate the effect of calcium phosphate bone cement on stability and strength of the fracture repair in a central depressed tibial plateau fracture cadaveric model.Paired human cadaveric tibial specimens.Biomechanics laboratory.Uniform pure depression fractures of lateral tibial plateau were created in twenty human cadaveric tibial specimens.The first part of the study used thirteen pairs of tibiae in two groups: a control group receiving the conventional treatment of morselized bone graft and two cancellous screws and an experimental group receiving calcium phosphate bone cement only. The second part of the study used seven pairs of tibiae in two experimental groups: one receiving calcium phosphate bone cement with a more extensive void preparation and the other group receiving calcium phosphate bone cement with a more extensive void preparation and two screws.Each tibia was loaded on a Material Testing Systems machine from twenty newtons to 250 newtons for 10,000 cycles to simulate immediate postoperative load transmission to the tibial plateau. Specimens were then loaded to failure to determine the ultimate strength of the reconstruction. Displacement of the articular fragment and stiffness at each cycle were measured during dynamic loading. Peak load, deformation at peak load, and resistance to depression were measured during the load to failure.The treatment of depressed tibia plateau fractures with a calcium phosphate cement provides equivalent or better stability than conventional open reduction and internal fixation in pure depression tibial plateau fractures. If the fracture void is prepared by eliminating the cancellous bone under the subchondral plate, the results are further improved.This study suggests that the non-weight-bearing postoperative period may be significantly reduced without clinically significant articular collapse.

    View details for Web of Science ID 000167717600008

    View details for PubMedID 11265011

  • Effect of cutting flute design on cortical bone screw insertion torque and pullout strength JOURNAL OF ORTHOPAEDIC TRAUMA Yerby, S., Scott, C. C., Evans, N. J., Messing, K. L., Carter, D. R. 2001; 15 (3): 216-221


    To determine the effect of the number and length of cutting flutes on the insertion torque and pullout strength for self-tapping 4.5-millimeter cortical bone screws.Screws were self-tapped in the diaphysis of human cadaver femurs. Each of the six screw types studied had different designs with varying cutting flute lengths and numbers. Bone mineral density, insertion torque, and pullout strength were measured.The study was conducted at an experimental biomechanics laboratory associated with a university medical center.Insertion torque and pullout strength were normalized by the local bone mineral density.The mean normalized insertion torque of the design with four full-length cutting flutes was less than the design with three full-length flutes and the two designs with one-third length flutes (p < 0.05). The mean normalized pullout strength of the screw with four full-length flutes was significantly greater than that of all screws with fewer than three flutes (p < 0.05).Priorities for a cutting flute design should ideally include ease of screw insertion, minimal soft tissue irritation, and maximal screw holding power. Screws with more than two flutes were easier to insert and did not cause cortical damage during insertion. The screw with four full-length flutes showed a trend toward being the easiest to insert and having the greatest holding strength.

    View details for Web of Science ID 000167717600011

    View details for PubMedID 11265014

  • Mechanobiology and joint conformity regulate endochondral ossification of sesamoids JOURNAL OF ORTHOPAEDIC RESEARCH Sarin, V. K., Carter, D. R. 2000; 18 (5): 706-712


    Sesamoid bones form by the endochondral ossification of sesamoid cartilages. This ossification process is thought to be similar to that responsible for the formation of secondary ossific nuclei in long-bone epiphyses. Sesamoids ossify much later in development than do epiphyses, however, and bone formation within sesamoids often begins by way of multiple ossific nuclei. Endochondral growth and ossification in the formation of secondary ossific nuclei have previously been correlated with distributions of the octahedral shear and hydrostatic stresses generated in vivo within cartilage anlagen. In this study, we used two-dimensional finite element analysis to predict the distributions of octahedral shear and hydrostatic stresses in an idealized model of a sesamoid cartilage subjected to in vivo loading. We examined the influence of sesamoid joint conformity. The distribution of an osteogenic stimulus was calculated with an approach similar to that used to predict epiphyseal ossification. The results suggest that, compared with conforming joints, nonconformity between the sesamoid cartilage and its articulating surface, which arises during early development, produces higher contact pressures within the sesamoid and leads to a thicker articular cartilage layer. For a nonconforming joint surface, the results suggest that ossification is favored anywhere within a broad internal region of the sesamoid, whereas a layer at the articular surface will remain cartilaginous. These findings highlight the subtle differences between ossification processes in epiphyses and sesamoids, indicating that the mechanical stress environment in sesamoids produces a diffuse stimulus leading to the onset of ossification and that the degree of joint nonconformity may influence the thickness of the articular cartilage layer.

    View details for Web of Science ID 000165616800004

    View details for PubMedID 11117290

  • Interpretation of calcaneus dual-energy X-ray absorptiometry measurements in the assessment of osteopenia and fracture risk JOURNAL OF BONE AND MINERAL RESEARCH Wren, T. A., Yerby, S. A., Beaupre, G. S., Carter, D. R. 2000; 15 (8): 1573-1578


    Dual-energy X-ray absorptiometry (DXA) of the calcaneus is useful in assessing bone mass and fracture risk at other skeletal sites. However, DXA yields an areal bone mineral density (BMD) that depends on both bone apparent density and bone size, potentially complicating interpretation of the DXA results. Information that is more complete may be obtained from DXA exams by using a volumetric density in addition to BMD in clinical applications. In this paper, we develop a simple methodology for determining a volumetric bone mineral apparent density (BMAD) of the calcaneus. For the whole calcaneus, BMAD = (BMC)/ADXA3/2, where BMC and ADXA are, respectively, the bone mineral content and projected area measured by DXA. We found that ADXA3/2 was proportional to the calcaneus volume with a proportionality constant of 1.82 +/- 0.02 (mean +/- SE). Consequently, consistent with theoretical predictions, BMAD was proportional to the true volumetric apparent density (rho) of the bone according to the relationship rho = 1.82 BMAD. Also consistent with theoretical predictions, we found that BMD varied in proportion to rho V1/3, where V is the bone volume. We propose that the volumetric apparent density, estimated at the calcaneus, provides additional information that may aid in the diagnosis of osteopenia. Areal BMD or BMD2 may allow estimation of the load required to fracture a bone. Fracture risk depends on the loading applied to a bone in relation to the bone's failure load. When DXA is used to assess osteopenia and fracture risk in patients, it may be useful to recognize the separate and combined effects of applied loading, bone apparent density, and bone size.

    View details for Web of Science ID 000088339000017

    View details for PubMedID 10934656

  • Tendon and ligament adaptation to exercise, immobilization, and remobilization JOURNAL OF REHABILITATION RESEARCH AND DEVELOPMENT Wren, T. A., Beaupre, G. S., Carter, D. R. 2000; 37 (2): 217-224


    This study provides a theoretical and computational basis for understanding and predicting how tendons and ligaments adapt to exercise, immobilization, and remobilization. In a previous study, we introduced a model that described the growth and development of tendons and ligaments. In this study, we use the same model to predict changes in the cross-sectional area, modulus, and strength of tendons and ligaments due to increased or decreased loading. The model predictions are consistent with the results of experimental exercise and immobilization studies performed by other investigators. These results suggest that the same fundamental principles guide both development and adaptation. A basic understanding of these principles can contribute both to prevention of tendon and ligament injuries and to more effective rehabilitation when injury does occur.

    View details for Web of Science ID 000165733400015

    View details for PubMedID 10850828

  • Mechanobiology in the development, maintenance, and degeneration of articular cartilage JOURNAL OF REHABILITATION RESEARCH AND DEVELOPMENT Beaupre, G. S., Stevens, S. S., Carter, D. R. 2000; 37 (2): 145-151


    During skeletal development, the establishment of a layer of cartilage at the ends of long bones is intimately linked to the process of endochondral ossification. Previous in vivo studies and computer models suggest that mechanobiological factors can play a key role in modulating cartilage growth and ossification. Specifically, intermittent hydrostatic pressure is thought to maintain cartilage, and shear stresses encourage cartilage destruction and ossification. In the present investigation we examined the combined effects of hydrostatic pressure and shear stress--in the form of an osteogenic index--on the development of a layer of articular cartilage, using an idealized finite element computer model. The results of our analyses provide further support for the view that mechanobiological factors play a key role in regulating the distribution of cartilage thickness and in maintaining a stable cartilage layer at maturity. The model predicts that joints that experience higher contact pressures will have thicker cartilage layers. These predictions are consistent with observations of cartilage thickness in both humans and animals. Variations in articular mechanical load are predicted to modulate cartilage thickness. These results are consistent with the view that the mechanobiological factors responsible for the development of diarthrodial joints eventually lead to cartilage degeneration and osteoarthritis (OA) with aging.

    View details for Web of Science ID 000165733400007

    View details for PubMedID 10850820

  • Mechanobiology of tendon adaptation to compressive loading through fibrocartilaginous metaplasia JOURNAL OF REHABILITATION RESEARCH AND DEVELOPMENT Wren, T. A., Beaupre, G. S., Carter, D. R. 2000; 37 (2): 135-143


    Tendons that wrap around bones often undergo fibrocartilaginous metaplasia. In this paper, we examine the biomechanical causes and consequences of this metaplasia. We propose an adaptation rule in which tissue permeability changes in response to local cyclic hydrostatic pressures associated with physical activity. The proposed rule predicts the development of a low-permeability region corresponding to the fibrocartilaginous region in a representative wrap-around tendon. A poroelastic finite element model is used to examine the time-dependent fluid pressures and compressive stresses and strains in the solid constituents of the tendon's extrafibrillar matrix. The low permeability in the adapted fibrocartilaginous region maintains fluid pressures, protecting the solid constituents of the tendon's extracellular matrix from high compressive stresses and strains that could disrupt the matrix organization. Adaptation through fibrocartilaginous metaplasia therefore allows wrap-around tendons to function effectively over a lifetime without sustaining excessive mechanical damage due to cyclic compressive loading.

    View details for Web of Science ID 000165733400006

    View details for PubMedID 10850819

  • Calcaneal loading during walking and running MEDICINE AND SCIENCE IN SPORTS AND EXERCISE Giddings, V. L., Beaupre, G. S., Whalen, R. T., Carter, D. R. 2000; 32 (3): 627-634


    This study of the foot uses experimentally measured kinematic and kinetic data with a numerical model to evaluate in vivo calcaneal stresses during walking and running.External ground reaction forces (GRF) and kinematic data were measured during walking and running using cineradiography and force plate measurements. A contact-coupled finite element model of the foot was developed to assess the forces acting on the calcaneus during gait.We found that the calculated force-time profiles of the joint contact, ligament, and Achilles tendon forces varied with the time-history curve of the moment about the ankle joint. The model predicted peak talocalcaneal and calcaneocuboid joint loads of 5.4 and 4.2 body weights (BW) during walking and 11.1 and 7.9 BW during running. The maximum predicted Achilles tendon forces were 3.9 and 7.7 BW for walking and running.Large magnitude forces and calcaneal stresses are generated late in the stance phase, with maximum loads occurring at approximately 70% of the stance phase during walking and at approximately 60% of the stance phase during running, for the gait velocities analyzed. The trajectories of the principal stresses, during both walking and running, corresponded to each other and qualitatively to the calcaneal trabecular architecture.

    View details for Web of Science ID 000085935000012

    View details for PubMedID 10731005

  • A model of mechanobiologic and metabolic influences on bone adaptation JOURNAL OF REHABILITATION RESEARCH AND DEVELOPMENT Hernandez, C. J., Beaupre, G. S., Carter, D. R. 2000; 37 (2): 235-244


    Bone adaptation, the process through which bone mass is modified in the body, plays a key role in the development of osteoporosis. Bone adaptation is known to be influenced by both mechanical and metabolic stimuli. Previous studies have concentrated on changes in bone adaptation caused by mechanical stimuli (mechanobiologic influences), yet current treatments for osteoporosis depend significantly on metabolic influences. We develop a theoretical model of bone adaptation that accounts for both mechanobiologic and metabolic influences. We demonstrate the utility of this model using a simulation of the cellular processes of bone adaptation on a representative volume of cancellous bone. Our long-term objective is the development of a more comprehensive computational model that will aid in the study of osteoporosis and other bone diseases.

    View details for Web of Science ID 000165733400017

    View details for PubMedID 10850830

  • Time-dependent effects of intermittent hydrostatic pressure on articular chondrocyte type II collagen and aggrecan mRNA expression JOURNAL OF REHABILITATION RESEARCH AND DEVELOPMENT Smith, R. L., Lin, J., Trindade, M. C., Shida, J., KAJIYAMA, G., Vu, T., Hoffman, A. R., van der Meulen, M. C., Goodman, S. B., Schurman, D. J., Carter, D. R. 2000; 37 (2): 153-161


    The normal loading of joints during daily activities causes the articular cartilage to be exposed to high levels of intermittent hydrostatic pressure. This study quantified effects of intermittent hydrostatic pressure on expression of mRNA for important extracellular matrix constituents. Normal adult bovine articular chondrocytes were isolated and tested in primary culture, either as high-density monolayers or formed aggregates. Loaded cells were exposed to 10 MPa of intermittent hydrostatic pressure at a frequency of 1 Hz for periods of 2, 4, 8, 12, and 24 hrs. Other cells were intermittently loaded for a period of 4 hrs per day for 4 days. Semiquantitative reverse transcription polymerase chain reaction assays were used to assess mRNA signal levels for collagen types II and I and aggrecan. The results showed that type II collagen mRNA signal levels exhibited a biphasic pattern, with an initial increase of approximately five-fold at 4 and 8 hrs that subsequently decreased by 24 hrs. In contrast, aggrecan mRNA signal increased progressively up to three-fold throughout the loading period. Changing the loading profile to 4 hrs per day for 4 days increased the mRNA signal levels for type II collagen nine-fold and for aggrecan twenty-fold when compared to unloaded cultures. These data suggest that specific mechanical loading protocols may be required to optimally promote repair and regeneration of diseased joints.

    View details for Web of Science ID 000165733400008

    View details for PubMedID 10850821

  • Mechanical influences on skeletal regeneration HUMAN BIOMECHANICS AND INJURY PREVENTION Carter, D. R., Polefka, E. G., Beaupre, G. S. 2000: 129-136
  • Coincident development of sesamoid bones and clues to their evolution ANATOMICAL RECORD Sarin, V. K., Erickson, G. M., Giori, N. J., Bergman, A. G., Carter, D. R. 1999; 257 (5): 174-180


    Sesamoid bones form within tendons in regions that wrap around bony prominences. They are common in humans but variable in number. Sesamoid development is mediated epigenetically by local mechanical forces associated with skeletal geometry, posture, and muscular activity. In this article we review the literature on sesamoids and explore the question of genetic control of sesamoid development. Examination of radiographs of 112 people demonstrated that the relatively infrequent appearances of the fabella (in the lateral gastrocnemius tendon of the knee) and os peroneum (in the peroneus longus tendon of the foot) are related within individuals (P < 0.01). This finding suggests that the tendency to form sesamoids may be linked to intrinsic genetic factors. Evolutionary character analyses suggest that the formation of these sesamoids in humans may be a consequence of phylogeny. These observations indicate that variations of intrinsic factors may interact with extrinsic mechanobiological factors to influence sesamoid development and evolution.

    View details for Web of Science ID 000083555500005

    View details for PubMedID 10597342

  • Computer model of endochondral growth and ossification in long bones: Biological and mechanobiological influences JOURNAL OF ORTHOPAEDIC RESEARCH Stevens, S. S., Beaupre, G. S., Carter, D. R. 1999; 17 (5): 646-653


    Endochondral growth and ossification, the processes by which cartilage increases in size and is replaced by bone, are affected by biological factors such as intrinsic genetic makeup and systemic chemical agents. In addition, these processes are affected by epigenetic mechanical factors: they may be accelerated in regions of intermittent high shear stress and decelerated in regions of intermittent high hydrostatic pressure. Previous models of bone development have not incorporated both biological and mechanobiological influences on endochondral growth and ossification. We have implemented a finite element analysis to model a developing bone rudiment from 8 weeks of gestational development to approximately 2 years after birth. As a function of time, we calculated a maturity index that reflects the progression of a region of cartilage through the endochondral ossification sequence of proliferation, hypertrophy, mineralization, and replacement by bone. We calculated a specific growth rate for each region of cartilage and estimated overall longitudinal growth of the rudiment. Regions of cartilage replaced by bone were remodeled. The results from the maturity index can be compared with distributions of proliferative, hypertrophic, and mineralized cartilage seen on histology at various stages in development. The results of the simulation predicted prenatal and postnatal developmental events, including formation of a secondary ossific nucleus, a layer of articular cartilage, and a growth plate. Our results demonstrate the necessity to include biological and mechanobiological influences when endochondral growth and ossification are considered.

    View details for Web of Science ID 000083717700004

    View details for PubMedID 10569472

  • Mechanically modulated cartilage growth may regulate joint surface morphogenesis JOURNAL OF ORTHOPAEDIC RESEARCH Heegaard, J. H., Beaupre, G. S., Carter, D. R. 1999; 17 (4): 509-517


    The development of normal joints depends on mechanical function in utero. Experimental studies have shown that the normal surface topography of diarthrodial joints fails to form in paralyzed embryos. We implemented a mathematical model for joint morphogenesis that explores the hypothesis that the stress distribution created in a functional joint may modulate the growth of the cartilage anlagen and lead to the development of congruent articular surfaces. We simulated the morphogenesis of a human finger joint (proximal interphalangeal joint) between days 55 and 70 of fetal life. A baseline biological growth rate was defined to account for the intrinsic biological influences on the growth of the articulating ends of the anlagen. We assumed this rate to be proportional to the chondrocyte density in the growing tissue. Cyclic hydrostatic stress caused by joint motion was assumed to modulate the baseline biological growth, with compression slowing it and tension accelerating it. Changes in the overall shape of the joint resulted from spatial differences in growth rates throughout the developing chondroepiphyses. When only baseline biological growth was included, the two epiphyses increased in size but retained convex incongruent joint surfaces. The inclusion of mechanobiological-based growth modulation in the chondroepiphyses led to one convex joint surface, which articulated with a locally concave surface. The articular surfaces became more congruent, and the anlagen exhibited an asymmetric sagittal profile similar to that observed in adult phalangeal bones. These results are consistent with the hypothesis that mechanobiological influences associated with normal function play an important role in the regulation of joint morphogenesis.

    View details for Web of Science ID 000082015400006

    View details for PubMedID 10459756

  • Biomechanical evaluation of fixation of intra-articular fractures of the distal part of the radius in cadavera: Kirschner wires compared with calcium-phosphate bone cement JOURNAL OF BONE AND JOINT SURGERY-AMERICAN VOLUME Yetkinler, D. N., Ladd, A. L., Poser, R. D., Constantz, B. R., Carter, D. 1999; 81A (3): 391-399


    The purpose of this study was to compare the biomechanical efficacy of an injectable calcium-phosphate bone cement (Skeletal Repair System [SRS]) with that of Kirschner wires for the fixation of intraarticular fractures of the distal part of the radius.Colles fractures (AO pattern, C2.1) were produced in ten pairs of fresh-frozen human cadaveric radii. One radius from each pair was randomly chosen for stabilization with SRS bone cement. These ten radii were treated with open incision, impaction of loose cancellous bone with use of a Freer elevator, and placement of the SRS bone cement by injection. In the ten control specimens, the fracture was stabilized with use of two horizontal and two oblique Kirschner wires. The specimens were cyclically loaded to a peak load of 200 newtons for 2000 cycles to evaluate the amount of settling, or radial shortening, under conditions simulating postoperative loading with the limb in a cast. Each specimen then was loaded to failure to determine its ultimate strength.The amount of radial shortening was highly variable among the specimens, but it was consistently higher in the Kirschner-wire constructs than in the bone fixed with SRS bone cement within each pair of radii. The range of shortening for all twenty specimens was 0.18 to 4.51 millimeters. The average amount of shortening in the SRS constructs was 50 percent of that in the Kirschner-wire constructs (0.51+/-0.34 compared with 1.01+/-1.23 millimeters; p = 0.015). With the numbers available, no significant difference in ultimate strength was detected between the two fixation groups.This study showed that fixation of an intra-articular fracture of the distal part of a cadaveric radius with biocompatible calcium-phosphate bone cement produced results that were biomechanically comparable with those produced by fixation with Kirschner wires. However, the constructs that were fixed with calcium-phosphate bone cement demonstrated less shortening under simulated cyclic load-bearing.

    View details for Web of Science ID 000079315300012

  • DXA-derived section modulus and bone mineral content predict long-bone torsional strength ACTA ORTHOPAEDICA SCANDINAVICA Sarin, V. K., Polefka, E. G., Beaupre, G. S., Kiratli, B. J., Carter, D. R., van der Meulen, M. C. 1999; 70 (1): 71-76


    Previous studies have used dual energy x-ray absorptiometry (DXA) scans to calculate the section modulus (Z) of adolescent and adult human femurs. The DXA-derived values of Z were assumed to be proportional to bone strength in bending and torsion. In this study we used dog (n 5), pig (n 4), and human (n 13) femurs covering a linear bone mineral content (BMCL) range of 0.91-6.1 g/cm. Using DXA scans, ex vivo torsional strength tests, and torsional finite element models, we assessed the validity of using the DXA-derived Z value as an indicator of strength. The correlation between BMCL and strength was r2 = 0.87 and the correlation between Z and strength was r2 = 0.86. Based on finite element results, the dog and pig section moduli were adjusted to be comparable to the human data based on cross-sectional shape and bone tissue shear strength differences. With these adjustments, the correlation between adjusted section modulus and measured strength did not improve (r2 = 0.87). These data indicate that DXA-derived section modulus can be used to predict strength over a wide range of bone sizes. However, a clear advantage of using DXA-derived section modulus rather than BMCL could not be found.

    View details for Web of Science ID 000079200100017

    View details for PubMedID 10191753

  • Mechanobiology of skeletal regeneration CLINICAL ORTHOPAEDICS AND RELATED RESEARCH Carter, D. R., Beaupre, G. S., Giori, N. J., Helms, J. A. 1998: S41-S55


    Skeletal regeneration is accomplished by a cascade of biologic processes that may include differentiation of pluripotential tissue, endochondral ossification, and bone remodeling. It has been shown that all these processes are influenced strongly by the local tissue mechanical loading history. This article reviews some of the mechanobiologic principles that are thought to guide the differentiation of mesenchymal tissue into bone, cartilage, or fibrous tissue during the initial phase of regeneration. Cyclic motion and the associated shear stresses cause cell proliferation and the production of a large callus in the early phases of fracture healing. For intermittently imposed loading in the regenerating tissue: (1) direct intramembranous bone formation is permitted in areas of low stress and strain; (2) low to moderate magnitudes of tensile strain and hydrostatic tensile stress may stimulate intramembranous ossification; (3) poor vascularity can promote chondrogenesis in an otherwise osteogenic environment; (4) hydrostatic compressive stress is a stimulus for chondrogenesis; (5) high tensile strain is a stimulus for the net production of fibrous tissue; and (6) tensile strain with a superimposed hydrostatic compressive stress will stimulate the development of fibrocartilage. Finite element models are used to show that the patterns of tissue differentiation observed in fracture healing and distraction osteogenesis can be predicted from these fundamental mechanobiologic concepts. In areas of cartilage formation, subsequent endochondral ossification normally will proceed, but it can be inhibited by intermittent hydrostatic compressive stress and accelerated by octahedral shear stress (or strain). Later, bone remodeling at these sites can be expected to follow the same mechanobiologic adaptation rules as normal bone.

    View details for Web of Science ID 000077173200007

    View details for PubMedID 9917625

  • An energy dissipation-based model for damage stimulated bone adaptation JOURNAL OF BIOMECHANICS Levenston, M. E., Carter, D. 1998; 31 (7): 579-586


    Based on experimental observations, several researchers have proposed a role for damage processes in stimulating an adaptive response in bone. In the current study we propose a model for bone adaptation based on cyclic energy dissipation as a measure of bone damage creation. By reanalyzing the fatigue data of Pattin et al. (1996), we derive a uniaxial form of the damage based formulation applicable to cortical regions experiencing primarily longitudinal stresses. Because of the experimentally observed difference between damage formation under tension and compression (Pattin et al., 1996), this formulation naturally predicts a difference in the adaptive response to tensile and compressive loading. This feature distinguishes the new formulation from existing strain energy based adaptation theories which treat tensile and compressive strains identically. Thus, developmental adaptation in response to unequal generation of damage provides one possible explanation for the experimentally observed difference between peak tensile and compressive bone surface strains.

    View details for Web of Science ID 000076346300001

    View details for PubMedID 9796679

  • Epigenetic mechanical factors in the evolution of long bone epiphyses ZOOLOGICAL JOURNAL OF THE LINNEAN SOCIETY Carter, D. R., Mikic, B., Padian, K. 1998; 123 (2): 163-178
  • Norian SRS cement augmentation in hip fracture treatment - Laboratory and initial clinical results CLINICAL ORTHOPAEDICS AND RELATED RESEARCH Goodman, S. B., Bauer, T. W., Carter, D., Casteleyn, P. P., Goldstein, S. A., Kyle, R. F., Larsson, S., Stankewich, C. J., Swiontkowski, M. F., Tencer, A. F., Yetkinler, D. N., Poser, R. D. 1998: 42-50


    Bone quality, initial fracture displacement, severity of fracture comminution, accuracy of fracture reduction, and the placement of the internal fixation device are important factors that affect fixation stability. New high strength cements that are susceptible to remodeling and replacement for fracture fixation may lead to improved clinical outcome in the treatment of hip fractures. Norian SRS is an injectable, fast setting cement that cures in vivo to form an osteoconductive carbonated apatite of high compressive strength (55 MPa) with chemical and physical characteristics similar to the mineral phase of bone. It can be used as a space filling internal fixation device to facilitate the geometric reconstruction, load transfer, and healing of bone with defects and/or fractures in regions of cancellous bone. Furthermore, this cement can improve the mechanical holding strength of conventional fixation devices. Use of this material potentially could improve fracture stability, retain anatomy during fracture healing and improve hip function, thus achieving better clinical outcomes. In vivo animal studies have shown the material's biocompatibility, and cadaveric studies have shown the biomechanical advantage of its use in hip fractures. Initial clinical experience (in 52 femoral neck fractures and 39 intertrochanteric fractures) showed the potential clinical use of this innovative cement in the treatment of hip fractures.

    View details for Web of Science ID 000072887000009

    View details for PubMedID 9553532

  • A microstructural model for the tensile constitutive and failure behavior of soft skeletal connective tissues JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME Wren, T. A., Carter, D. R. 1998; 120 (1): 55-61


    We propose a microstructural model for the uniaxial tensile constitutive and failure behavior of soft skeletal connective tissues. The model characterizes the tissues as two-phase composites consisting of collagen fibers embedded in ground substance. Nonlinear toe region behavior in the stress versus strain curve results from the straightening of crimped fibers and from fiber reorientation. Subsequent linear behavior results from fiber stretching affected by fiber volume fraction, collagen type, crosslink density, and fiber orientation. Finally, the tissue fails when fibers successively rupture at their ultimate tensile strain. We apply the model to tendon, meniscus, and articular cartilage. The model provides a consistent approach to modeling the tensile behavior of a wide range of soft skeletal connective tissues.

    View details for Web of Science ID 000072307300010

    View details for PubMedID 9675681

  • A model for loading-dependent growth, development, and adaptation of tendons and ligaments JOURNAL OF BIOMECHANICS Wren, T. A., Beaupre, G. S., Carter, D. R. 1998; 31 (2): 107-114


    The geometric and material properties of tendons and ligaments change during growth and development. While some of the changes occur in the absence of mechanical loading, normal development requires the mechanical stimulus provided by normal physical activity. We have developed an analytical framework for quantitatively describing changes in uniaxial tendon and ligament properties throughout ontogeny. In our approach, cross-sectional area, modulus, and strength undergo baseline levels of development due to inherent time-dependent biological influences. The properties also change in response to mechanobiological influences by adapting to maintain a constant daily strain stimulus under changing load conditions. We have implemented a computer algorithm based on these concepts and obtained results consistent with experimental observations of normal tendon and ligament growth and development reported by other investigators. Additional results suggest that these concepts can also explain tendon and ligament adaptation to increased or decreased loading experienced during development.

    View details for Web of Science ID 000073974800001

    View details for PubMedID 9593203

  • Mechanobiologic regulation of osteogenesis and arthrogenesis SKELETAL GROWTH AND DEVELOPMENT: CLINICAL ISSUES AND BASIC SCIENCE ADVANCES Carter, D. R., van der Meulen, M., Beaupre, G. S. 1998: 99-130
  • Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations JOURNAL OF BIOMECHANICS Jacobs, C. R., SIMO, J. C., Beaupre, G. S., Carter, D. R. 1997; 30 (6): 603-613


    Over 100 years ago, Wolff hypothesized that cancellous bone altered both its apparent density and trabecular orientation in response to mechanical loads. A mathematical counterpart of this principle is derived by adding a remodeling rule for the rate-of-change of the full anisotropic stiffness tensor (all 21 independent terms) to the density rate-of-change rule adapted from an existing isotropic theory. As a result, anisotropy and density patterns develop such that the local stiffness tensor is optimal for the given series of applied loadings. The method does not rely on additional morphological measures of trabecular orientation. Furthermore, assumptions of material symmetry are not required, and any observed regions of orthotropy, transverse isotropy, or isotropy are a result entirely of the functional adaptation of the bone and not the consequence of a modeling assumption. This approach has been implemented with the finite element method and applied to a two-dimensional model of the proximal femur with encouraging results.

    View details for Web of Science ID A1997WZ33100009

    View details for PubMedID 9165394

  • Correspondence between theoretical models and dual energy x-ray absorptiometry measurements of femoral cross-sectional growth during adolescence JOURNAL OF ORTHOPAEDIC RESEARCH VANDERMEULEN, M. C., Marcus, R., Bachrach, L. K., Carter, D. R. 1997; 15 (3): 473-476


    We have developed an analytical model of long bone cross-sectional ontogeny in which appositional growth of the diaphysis is primarily driven by mechanical stimuli associated with increasing body mass during growth and development. In this study, our goal was to compare theoretical predictions of femoral diaphyseal structure from this model with measurements of femoral bone mineral and geometry by dual energy x-ray absorptiometry. Measurements of mid-diaphyseal femoral geometry and structure were made previously in 101 Caucasian adolescents and young adults 9-26 years of age. The data on measured bone mineral content and calculated section modulus were compared with the results of our analytical model of cross-sectional development of the human femur over the same age range. Both bone mineral content and section modulus showed good correspondence with experimental measurements when the relationships with age and body mass were examined. Strong linear relationships were evident for both parameters when examined as a function of body mass.

    View details for Web of Science ID A1997XN54600022

    View details for PubMedID 9246096

  • Observations of convergence and uniqueness of node-based bone remodeling simulations ANNALS OF BIOMEDICAL ENGINEERING Fischer, K. J., Jacobs, C. R., Levenston, M. E., Carter, D. R. 1997; 25 (2): 261-268


    Some investigators have indicated that mathematical theories and computational models of bone adaptation may not converge and that the density solutions from such simulations are dependent on the initial density distribution. In this study, two-dimensional finite element models were used to investigate the effect of initial density distribution on the final density distribution produced using a node-based bone remodeling simulation. The first model was a generic long bone, and the second was a proximal femur, For each model, we conducted time-dependent, node-based, linear rate-law bone remodeling simulations. Five initial density conditions were used with the generic long bone and three with the proximal femur. Remodeling simulations were performed, and the largest average nodal density differences at the end of the simulations were 0.000010 g/cm3 and 0.000006 g/cm3 for the generic long bone and proximal femur models, respectively. Results illustrate that, for a given set of loads and a given finite element model, the node-based bone adaptation algorithm can yield a unique density distribution. In conjunction with previous studies, this finding suggests that uniqueness of the density solution is dependent on both the mathematical theory and the computational implementation.

    View details for Web of Science ID A1997WN69400003

    View details for PubMedID 9084831

  • Body mass is the primary determinant of midfemoral bone acquisition during adolescent growth BONE Moro, M., VANDERMEULEN, M. C., Kiratli, B. J., Marcus, R., Bachrach, L. K., Carter, D. R. 1996; 19 (5): 519-526


    To study the determinants of bone mass and structure during adolescence, we analyzed the femoral mid-diaphysis of 375 healthy adolescents and young adults, ages 9-26 years, from four ethnic cohorts (African-American, Asian-American, Caucasian, and Hispanic). Whole-body dual-energy X-ray absorptiometry (DXA) scans were used to determine diaphyseal length and mid-diaphyseal diameter of the left femur, as well as linear bone mineral content (BMCL) of a region at the mid-diaphysis. Cross-sectional geometric properties were estimated and used to calculate two structural strength indicators: the section modulus and the whole bone strength index. When the relationships between the bone measurements and age, pubertal group, height, or body mass were evaluated, all cross-sectional femoral measures correlated most strongly with body mass. Multiple regressions accounting for gender and ethnicity provided little additional predictive value over the simple regressions with body mass alone. Furthermore, accounting for all developmental parameters (age, pubertal group, body mass, lean body mass, calcium intake, physical activity level) as well as ethnicity and gender in a single saturated model also did not generally significantly improve the predictive results achieved using only body mass. Our results indicate that increases in midfemoral bone mass and cross-sectional properties during adolescence are primarily related to increases in mechanical loading as reflected by body mass.

    View details for Web of Science ID A1996VR34700014

    View details for PubMedID 8922652

  • Bite-force estimation for Tyrannosaurus rex from tooth-marked bones NATURE Erickson, G. M., VANKIRK, S. D., Su, J. T., Levenston, M. E., CALER, W. E., Carter, D. R. 1996; 382 (6593): 706-708
  • Different loads can produce similar bone density distributions BONE Fischer, K. J., Jacobs, C. R., Levenston, M. E., Carter, D. R. 1996; 19 (2): 127-135


    Finite element models of a generic long bone and the proximal femur were used to identify important load characteristics and to determine whether small changes in load affect bone adaptation simulations. We also examined the effect of implants on the sensitivity of bone adaptation simulations to changes in loads. For each model, a primary load set was selected and incorporated in a bone adaptation simulation to generate a primary density distribution. A density-based load estimation method was used to determine a secondary set of loading conditions for each model. Each secondary load set was incorporated in a bone adaptation simulation and the resulting density distribution was compared to the corresponding primary density distribution. Nearly identical density distributions were produced for the natural generic long bone model (average nodal density difference 0.02 g/cm3). For the natural proximal femur model, the density distributions were very similar, but differences were apparent (average nodal density difference 0.07 g/cm3). The same primary and secondary load sets were used for bone adaptation simulations with implant models. For the proximal femur model, density distribution differences with the implant were very slightly less than those of the natural model. For the generic long bone model, the implant amplified differences between density distributions (average nodal density difference 0.14 g/cm3). Thus, variations in loading conditions may partially explain variations in long-term total joint outcome. The total equivalent stimulus load magnitudes for the two load sets for the generic long bone model were within 1%, and the stimulus-weighted average load directions were within 1 degree. The similarity of these parameters and the natural generic long bone density distributions indicate that the overall magnitude and average load direction are key factors affecting bone adaptation.

    View details for Web of Science ID A1996VB74000008

    View details for PubMedID 8853856

  • Mechanical and geometric changes in the growing femora of BMP-5 deficient mice BONE Mikic, B., VANDERMEULEN, M. C., KINGSLEY, D. M., Carter, D. R. 1996; 18 (6): 601-607


    We examined the growth-related changes in femoral geometry and torsional strength in BMP-5 deficient short-ear mice over a 22-week time interval ("long-term" changes). Four groups of female mice (n = 6 per group) were examined: short-ear animals and their heterozygous control littermates at 4 and 26 weeks of age. In agreement with findings previously observed in a mixed-gender group of adult mice (26 weeks), the femora of short-ear animals were significantly smaller in length and cross section at both ages. The magnitudes of the differences between genotypes were comparable at each age, indicating that the overall rates of appositional and endochondral growth were similar for both genotypes over the 22-week period. In the adult animals, short-ear femora were 27 +/- 7% weaker in torsional strength due to their smaller cross-sectional geometry. However, bone strength in adult short-ear mice appeared to be adequate for animal size: No significant difference was detected in maximum femoral torque when normalized by body mass. In 4-week old animals, BMP-5 deficiency was associated with a 27 +/- 6% lower body mass, but the torsional strength of the femur was not significantly different from that of controls. Cross-sectional geometry was smaller in 4-week old short-ear mice, but the apparent bone material ultimate shear stress was elevated by 33 +/- 10%, thereby resulting in a whole bone torsional strength equivalent to that of the larger control mice. While the data suggest a higher material strength in the 4-week-old short-ear animals, no significant difference in the level of bone mineralization was detectable between genotypes at either age.

    View details for Web of Science ID A1996UT99700017

    View details for PubMedID 8806002

  • Untitled JOURNAL OF BIOMECHANICS Giori, N. J., Beaupre, G. S., Carter, D. R. 1996; 29 (4): 573-573
  • Stress governs tissue phenotype at the femoral insertion of the rabbit MCL. Journal of biomechanics Giori, N. J., Beaupré, G. S., Carter, D. R. 1996; 29 (4): 573-574

    View details for PubMedID 8964789

  • Cyclic mechanical property degradation during fatigue loading of cortical bone JOURNAL OF BIOMECHANICS Pattin, C. A., CALER, W. E., Carter, D. R. 1996; 29 (1): 69-79


    Fatigue damage accumulation has been demonstrated in living bone and postulated as a stimulus to the bone modeling and remodeling response. Mechanical property degradation is one manifestation of fatigue damage accumulation. This study examines changes in secant modulus and cyclic energy dissipation behavior during axial load-controlled fatigue loading of cortical bone specimens. The findings suggest that secant modulus degradation and cyclic energy dissipation are greatly increased at loading levels above critical damage strain thresholds of 2500 and 4000 mu epsilon in tensile and compressive fatigue, respectively. Tensile and compressive fatigue loading also caused different forms of modulus degradation at loading levels above these thresholds. Bone behaves as a linear viscoelastic material below these thresholds, even after prior property degradation at higher loading levels. Cyclic energy dissipation was proportional to the 2.1 power of the applied effective strain range for all loadings below 2500 mu epsilon. Above 2500 mu epsilon, tensile fatigue loading caused cyclic energy dissipation proportional to the 5.8 power of the applied effective strain range. Compressive fatigue loading dissipated cyclic energy proportional to the 4.9 power of applied effective strain range over 4000 mu epsilon. Lifetime energy dissipation over all fatigue tests to fracture at a single loading level was well fitted by the same power law in the number of cycles to failure raised to the 0.6 power. Loading levels of 2500 mu epsilon in tension and 4000 mu epsilon in compression are within the ranges observed in living animals, and thus these phenomena may play a role in initiating the remodeling response in live bone tissue.

    View details for Web of Science ID A1996TM44400009

    View details for PubMedID 8839019

  • Mechanical factors in bone growth and development. Bone Carter, D. R., van der Meulen, M. C., Beaupré, G. S. 1996; 18 (1): 5S-10S


    Mechanobiologic factors strongly influence skeletal ossification and regulate changes in bone geometry and apparent density during ontogeny. We have developed computer models that implement a simple mathematical rule relating cyclic tissue stresses to bone apposition and resorption. Beginning at the fetal stages of the femoral anlage, these models successfully predict the appositional bone growth and modeling observed in the development of the diaphyseal cross section. The same basic mechanobiologic rule can also predict the architectural construction of the proximal cancellous bone formed in regions of endochondral ossification. Geometry and density changes in adult diaphyseal and cancellous bone as a result of changes in physical activity can be simulated by invoking the same rule used during development. Future clinical and experimental work is needed to provide more quantitative data for mechanobiologic rules and elucidate the interactions between chemical and mechanical factors influencing bone biology.

    View details for PubMedID 8717541

  • Determinants of femoral geometry and structure during adolescent growth JOURNAL OF ORTHOPAEDIC RESEARCH VANDERMEULEN, M. C., Ashford, M. W., Kiratli, B. J., Bachrach, L. K., Carter, D. R. 1996; 14 (1): 22-29


    Our goal was to understand developmental determinants of femoral structure during growth and sexual maturation by relating femoral measurements to gender and developmental factors (age, pubertal stage, height, and body mass). The bone mineral content of the femur was measured by dual energy x-ray absorptiometry in 101 healthy Caucasian adolescents and young adults, 9-26 years of age. After some simplifying assumptions had been made, cross-sectional geometric properties of the femoral midshaft were estimated. Two geometry-based structural indicators, the section modulus and whole bone strength index, were calculated to assess the structural characteristics of the femur. Femoral strength, as described by these structural indicators, increased dramatically from childhood through young adulthood. Regressions were performed between these femoral measurements and the developmental factors. Our data show that of age, pubertal stage, body mass, and height, body mass is the strongest predictor of femoral cross-sectional properties, and the correlation of body mass with femoral cross-sectional structure is independent of gender. A model including all four developmental factors and gender did not substantially increase the accuracy of predictions compared with the model with body mass alone. In light of previous research, we hypothesize that body mass is an indicator of in vivo loading and that this in vivo loading influences the cross-sectional growth of the long bones.

    View details for Web of Science ID A1996UA58800005

    View details for PubMedID 8618162

  • In vitro stimulation of articular chondrocyte mRNA and extracellular matrix synthesis by hydrostatic pressure JOURNAL OF ORTHOPAEDIC RESEARCH Smith, R. L., RUSK, S. F., Ellison, B. E., Wessells, P., Tsuchiya, K., Carter, D. R., CALER, W. E., Sandell, L. J., Schurman, D. J. 1996; 14 (1): 53-60


    This study tested the effects of hydrostatic pressure (10 MPa) on adult articular chondrocyte mRNA and extracellular matrix synthesis in vitro. High density primary cultures of bovine chondrocytes were exposed to hydrostatic pressure applied intermittently at 1 Hz or constantly for 4 hours in serum-free medium or in medium containing 1% fetal bovine serum. mRNAs for aggrecan, types I and II collagen, and beta-actin were analyzed by Northern blots and quantified by slot blots. Proteoglycan synthesis was quantified by 35SO4 uptake into cetylpyridinium chloride-precipitable glycosaminoglycans, and cell-associated aggrecan and type-II collagen were detected by immunohistochemical techniques. In serum-free medium, intermittent pressure increased aggrecan mRNA signal by 14% and constant pressure decreased type-II collagen mRNA signal by 16% (p < 0.05). In the presence of 1% fetal bovine serum, intermittent pressure increased aggrecan and type-II collagen mRNA signals by 31% (p < 0.01) and 36% (p < 0.001), respectively, whereas constant pressure had no effect on either mRNA. Intermittent and constant pressure stimulated glycosaminoglycan synthesis 65% (p < 0.001) and 32% (p < 0.05), respectively. Immunohistochemical detection of cell-associated aggrecan and type-II collagen was increased in response to both intermittent and constant pressure. These data support the hypothesis that physiologic hydrostatic pressure directly influences the extracellular matrix metabolism of articular chondrocytes.

    View details for Web of Science ID A1996UA58800009

    View details for PubMedID 8618166

  • Effects of fluid-induced shear on articular chondrocyte morphology and metabolism in vitro JOURNAL OF ORTHOPAEDIC RESEARCH Smith, R. L., Donlon, B. S., Gupta, M. K., Mohtai, M., Das, P., Carter, D. R., Cooke, J., Gibbons, G., Hutchinson, N., Schurman, D. J. 1995; 13 (6): 824-831


    This study tested the effects of fluid-induced shear on high density monolayer cultures of adult articular chondrocytes. Fluid-induced shear (1.6 Pa) was applied by cone viscometer to normal human and bovine articular chondrocytes for periods of 24, 48, and 72 hours. At 48 and 72 hours, fluid-induced shear caused individual chondrocytes to elongate and align tangential to the direction of cone rotation. Fluid-induced shear stimulated glycosaminoglycan synthesis by 2-fold (p < 0.05) and increased the length of newly synthesized chains in human and bovine chondrocytes. In human chondrocytes, the hydrodynamic size of newly synthesized proteoglycans also was increased. After 48 hours of fluid-induced shear, the release of prostaglandin E2 from the chondrocytes was increased 10 to 20-fold. In human chondrocytes, mRNA signal levels for tissue inhibitor of metalloproteinase increased 9-fold in response to shear compared with the controls. In contrast, mRNA signal levels for the neutral metalloproteinases, collagenase, stromelysin, and 72 kD gelatinase, did not show such major changes. This study demonstrated that articular chondrocyte metabolism responds directly to physical stimulation in vitro and suggests that mechanical loading may directly influence cartilage homeostasis in vivo.

    View details for Web of Science ID A1995TQ03900003

    View details for PubMedID 8544017



    Growth, functional adaptation, and torsional strength were examined in the femora of 39-day-old male Sprague-Dawley rats subjected to hindlimb suspension for 0, 1, 2, 3, or 4 weeks and were compared with measurements for age-matched control animals. Our goal was to understand the effect of reduced loading on the normal age-related changes in femoral properties during growth. The control animals exhibited growth-related increases in all geometric and torsional properties of the femur. The mean body mass and femoral length of the hindlimb-suspended rats were similar to those of the controls throughout the experiment. Over 4 weeks, the femoral cross-sectional and torsional measurements from the hindlimb-suspended rats demonstrated increases in comparison with the basal values (+33% cross-sectional area, +64% polar moment of inertia, +67% ultimate torque, and +181% torsional rigidity), but the age-matched controls showed significantly greater growth-related increases (+71% cross-sectional area, +136% polar moment of inertia, +127% ultimate torque, and +367% torsional rigidity). The differences in femoral structural strength between the hindlimb-suspended animals and the age-matched controls were attributable to differences in altered cross-sectional geometry.

    View details for Web of Science ID A1995TH31500008

    View details for PubMedID 7472748



    Retrieval studies have shown that tissue at the bone-cement or bone-implant interface can develop into fibrous tissue, fibrocartilage, and bone, and that tissue differentiation appears to be mechanically influenced. A prior histologic analysis of retrieved interface tissues supporting cemented Marmor unicondylar knee components found that beneath the central portion of these implants, a thick, mature layer of fibrocartilage consistently developed, whereas fibrous tissue formed beneath the prosthesis periphery and adjacent to the bone beneath the tibial spine. Finite-element analysis was used to model the interface tissue supporting a cemented Marmor tibial component and interpreted patterns of stress and strain generated in the interface according to a mechanically based tissue differentiation theory. Distortional strain and hydrostatic stress, mechanical stimuli that are hypothesized to be associated with fibrous matrix and cartilaginous matrix production, respectively, were found to correlate well with the previous histologic findings. Given the biologic environments in which the retrieved interface tissues developed, frequently applied hydrostatic stress of approximately 0.7 MPa may be sufficient to stimulate cartilaginous extracellular matrix production in the interface tissue, and frequently applied distortional strain of 10% may be sufficient to stimulate fibrous extracellular matrix production.

    View details for Web of Science ID A1995RT19900017

    View details for PubMedID 8523012



    Bone morphogenetic proteins (BMPs) play a critical role in early skeletal development. BMPs are also potential mediators of bone response to mechanical loading, but their role in later stages of bone growth and adaptation has yet to be studied. We characterized the postcranial skeletal defects in mature mice with BMP deficiency by measuring hind-limb muscle mass and long bone geometric, material, and torsional mechanical properties. The animals studied were 26-week-old short ear mice (n = 10) with a homozygous deletion of the BMP-5 gene and their heterozygous control litter mates (n = 15). Gender-related effects, which were found to be independent of genotype, were also examined. The femora of short ear mice were 3% shorter than in controls and had significantly lower values of many cross-sectional geometric and structural strength parameters (p < 0.05). No significant differences in ash content or material properties were detected. Lower femoral whole bone torsional strength was due to the smaller cross-sectional geometry (16% smaller section modulus) in the short ear mice. The diminished cross-sectional geometry may be commensurate with lower levels of in vivo loading, as reflected by body mass (-8%) and quadriceps mass (-11%). While no significant gender differences were found in whole bone strength or cross-sectional geometry, males had significantly greater body mass (+18%) and quadriceps mass (+15%) and lower tibio-fibular ash content (-3%). The data suggest that adult female mice have a more robust skeleton than males, relative to in vivo mechanical demands. Furthermore, although the bones of short ear mice are smaller and weaker than in control animals, they appear to be biomechanically appropriate for the in vivo mechanical loads that they experience.

    View details for Web of Science ID A1995RB63900005

    View details for PubMedID 7605705



    The in vivo implantation of strain gages on the surface of bones has proven to be a very useful technique for studying the relationship between in vivo loading and bone growth and adaptation. However, data from such experiments have yet to be well incorporated within the context of theoretical models of bone adaptation. Methods for analyzing bone rosette strain gage recordings within the framework of strain energy density-based computational modeling/remodeling theories are presented. A new strain energy density based parameter, energy equivalent strain, is proposed as a single scalar measure of cyclic strain magnitudes and the concept of a daily strain stimulus is also introduced. As an illustrative example, the approach is applied to analyze previously reported in vivo data from the anteromedial human tibia (Lanyon et al., 1975, Acta orthop. Scand. 46, 256-268).

    View details for Web of Science ID A1995QM53600012

    View details for PubMedID 7738056



    Evolutionary and developmental factors responsible for the scaling relationships observed in animal skeletons are poorly understood. We have created a mathematical model for long bone cross-sectional development which incorporates both intrinsic growth and extrinsic, adaptive bone modeling in response to changes in bone mechanical strains during ontogeny. The model successfully simulates the developing morphology in individual animals and the bone geometric allometric relationships among adults across many species (range from mouse to elephant in size). Our results suggest that long bone scaling characteristics are not a result of intrinsic genetic factors but are the results of highly conserved, extrinsic biophysical processes whereby bone tissue strains modulate skeletal morphogenesis.

    View details for Web of Science ID A1995QK02400004

    View details for PubMedID 7715201

  • THE ROLE OF LOADING MEMORY IN BONE ADAPTATION SIMULATIONS BONE Levenston, M. E., Beaupre, G. S., Jacobs, C. R., Carter, D. R. 1994; 15 (2): 177-186


    The concept that bone responds to a time-averaged value of its current mechanical loading forms the basis for many computational bone adaptation algorithms. Some mathematical formulations have incorporated a quantification of the loading experienced during a single "average" day and thus implicitly assume that bone responds abruptly to changes in its loading history. To better reflect the time delays inherent in bone cell recruitment and activation processes, we included a fading memory of past loading. Implementing an exponentially fading memory with time constants of 5, 20, and 100 days, we simulated bone adaptations to abrupt and gradual changes in mechanical loading. Both an idealized single degree-of-freedom model and a finite element model of the proximal femur were studied. A time constant of 5 days produced time-dependent density changes that were negligibly different from those of the standard approach without memory. Models with higher time constants produced significant transient time lags (up to 8.1% difference) in the predicted short-term (3 months) bone density changes. A time constant of 100 days produced overshoots (by approximately 1%) of the eventual steady-state. All models predicted comparable long-term (after several years) steady-state adaptations. Future experimental analyses will be necessary to better determine appropriate fading memory time constants for bone under various loading conditions.

    View details for Web of Science ID A1994NE28000006

    View details for PubMedID 8086235

  • Computer simulations of stress-related bone remodeling around noncemented acetabular components. journal of arthroplasty Levenston, M. E., Beaupré, G. S., Schurman, D. J., Carter, D. R. 1993; 8 (6): 595-605


    The authors have used computer modeling techniques to examine stress-related bone changes in the acetabular region. Using a previously developed theory for bone development and adaptation, the authors simulated the distribution of bone density in the natural pelvis as well as changes in bone density following total hip arthroplasty. The geometry of the finite element model was based on a two-dimensional slice through the pelvis. Starting from a solid, homogeneous structure, the computer simulations predicted the distribution of bone density throughout the natural pelvis. The predicted bone density distribution in this first simulation agreed well with the actual bone density distribution only when loads representing multiple activities were incorporated. Using the predicted density distribution as a starting point the authors modified the finite element models to study two designs of noncemented, metal-backed acetabular cups. The simulations with fully fixed bone-implant interfaces predicted extensive loss of bone density medial and inferior to the prosthetic components. The simulations with loose interfaces led to more moderate losses of bone density, indicating a load transfer more similar to that which occurs in the natural joint. The differences in simulated bone remodeling between the two component designs were quite minimal. These results indicate that acetabular components with full bony ingrowth may induce significant stress-related bone remodeling due to a nonphysiologic transfer of load.

    View details for PubMedID 8301277



    We developed a computer model to simulate the interaction of biological and mechanobiological factors in the development of the cross-sectional morphology of long bones. The model incorporated a strong influence of biologically induced bone formation during early development. In addition, an assumed mechanical loading history during growth and development corresponding to age-related changes in body weight and muscle mass was applied. Based on the bone stress stimulus generated by the assumed loads, mechanically induced apposition and resorption rates were calculated at the periosteal and endosteal surfaces using a previously developed bone modeling theory. These methods successfully emulated the growth-related changes seen in long bone diaphyseal structure as well as changes observed in mature bones during aging. The simulations recreated the rapid increase in bone dimensions during development, stabilizing at maturity, and then the gradual, age-related subperiosteal expansion and cortical thinning. Throughout the growth, development, and aging simulations, the values of the bone radii, area, moments of inertia, and apposition rates corresponded well with measurements documented by other researchers.

    View details for Web of Science ID A1993LK84600005

    View details for PubMedID 8274306



    In vivo studies have suggested that mechanical factors are involved in the regulation of the morphology and biochemical composition of tendons that wrap around bones. In these tendons, fibrocartilage is found in the segment wrapped around the bone, and tendon far from the bone displays normal tendon histomorphology. Recent in vitro studies have shown that intermittently loaded connective tissue cells are sensitive to changes in cellular shape and hydrostatic pressure: stretching and distortion of the cells enhances production of fibrous matrix and hydrostatic pressure enhances production of cartilaginous matrix. We used finite-element analysis to determine whether the regions of increased development of cartilaginous matrix in tendons that wrap around bones correspond to regions in which tendon cells are subjected to higher pressures, and whether the maintenance and rearrangement of fibrous extracellular matrix in these tendons is associated with regions of stretching and distortion of cells. We found that regions of cartilaginous matrix and fibrous matrix formation and turnover correlate well with patterns of hydrostatic compressive stress and distortional strain in the tendon. Although further experiments clearly are needed to establish the predictive value of our approach, hydrostatic stress and distortional strain history--parameters intimately related to changes in cellular pressure and shape, respectively--appear to be important tissue-level mechanical stimuli that regulate cartilaginous and fibrous matrix composition of connective tissues.

    View details for Web of Science ID A1993LQ68800012

    View details for PubMedID 8340830



    The role of in vivo mechanical loading histories in normal skeletogenesis is related to the process of adaptive, stress-regulated bone remodeling in the adult. The results of many previous computer models for endochondral ossification and bone modeling and remodeling are reviewed. These studies support the view that simple stress-related mathematical algorithms or "construction rules" can be used to emulate normal skeletal development and architectural construction. Such mathematical rules presumably represent the net result of biophysical phenomena influencing cell metabolism and biosynthetic activity. These rules are also successful in describing the adaptation of adult bone to changes in tissue stresses. The findings suggest that stress-related functional adaptation in mature bones may be merely the adult manifestation of the same mechanical construction rules that guide and constrain normal development.

    View details for Web of Science ID A1992KF28700004

    View details for PubMedID 1485546



    A substantial body of cross-sectional data and a smaller number of intervention trials generally justify optimism that regular physical activity benefits the skeleton. We conducted an 8 month controlled exercise trial in a group of healthy college women (mean age = 19.9 years) who were randomly assigned to a control group or to progressive training in jogging or weight lifting. We measured the following variables: bone mineral density (BMD) of the spine (L2-4) and right proximal femur using dual-energy x-ray absorptiometry, dynamic muscle strength using the 1-RM method, and endurance performance using the 1.5 mile walk/run field test. A total of 31 women completed the 8 month study. For women completing the study, compliance, defined as the percentage of workout sessions attended, was 97% for the runners (range 90-100%) and 92% (range 88-100%) for the weight trainers. Body weight increased by approximately 2 kg in all groups (p less than 0.05). Weight training was associated with significant increases (p less than 0.01) in muscle strength in all muscle groups. Improvement ranged from 10% for the deep back to 54% for the leg. No significant changes in strength scores were observed in the control or running groups. Aerobic performance improved only in the running group (16%, p less than 0.01). Lumbar BMD increased (p less than 0.05) in both runners (1.3 +/- 1.6%) and weight trainers (1.2 +/- 1.8%). These results did not differ from each other but were both significantly greater than results in control subjects, in whom bone mineral did not change.(ABSTRACT TRUNCATED AT 250 WORDS)

    View details for Web of Science ID A1992JD68000005

    View details for PubMedID 1642145



    Bone densitometry using dual-photon absorptiometry (DPA) or dual-energy x-ray absorptiometry (DXA) has become a standard method for assessing bone mineral content in the spine and other skeletal regions. A projected areal density, referred to as bone mineral density (BMD,g/cm2), is normally calculated to assess regional bone density and strength. We demonstrate that this measure can be misleading when used to compare bones of different sizes due to inherent biases caused by bone thickness differences. For example, assuming that volumetric bone density remains constant and bony linear dimensions are proportional to height, a 20% increase in height would result in a 20% increase in both the thickness and the BMD of any bone. We describe new analysis methods to reduce the confounding effect of bone size, and we introduce a parameter, bone mineral apparent density (BMAD, g/cm3), that better reflects bone apparent density. Using this parameter, we calculate a quantity that serves as an index of bone strength (IBS, g2/cm4) for whole vertebral bodies. These analyses were applied to lumbar spine (L2-4) DXA measurements in a population of women 17-40 years old and appear to offer advantages to conventional techniques.

    View details for Web of Science ID A1992HD57300003

    View details for PubMedID 1570758



    This study analyzed processes underlying osteoporosis and osteoarthrosis after short-term immobilization of the right hind limb of postadolescent (2.8 kg) and mature (4.0 kg) rabbits. After 3 weeks, the lateral posterior aspect of the lateral tibial plateau and the lateral femoral condyle of the immobilized limb exhibited prominent subchondral vascular eruptions. Femoral metaphyseal bone density decreased 27 and 18% in the immobilized limbs of postadolescent and mature rabbits, respectively. Calcein green fluorescence increased 1.9-fold (p less than 0.001) in the metaphyseal trabeculae of immobilized femurs. With immobilization, sulfate incorporation into femoral cartilage glycosaminoglycan increased, although total cartilage glycosaminoglycan and hydroxyproline levels were unchanged. Thymidine incorporation into DNA increased four- to fivefold in tibial and femoral cartilage of the immobilized limb. In this study, bone loss and remodeling preceded erosive cartilage degradation.

    View details for Web of Science ID A1992GX48200010

    View details for PubMedID 1370179

  • In vitro study of initial stability of a conical collared femoral component. journal of arthroplasty Fischer, K. J., Carter, D. R., Maloney, W. J. 1992; 7: 389-395


    This in vitro experimental study compared the initial stability of an uncemented conical collared femoral component to that of the same component with the collar removed. The two configurations examined simulated joint resultant forces encountered in single leg stance and stair climbing. For the simulated single leg stance loads, the data do not allow any inferences about relative component stability. With the exception of one collarless control, all micromotion for single leg stance loading was under 150 microns, measured approximately 1.5 cm below the resection line. For scaled stair-climbing loads, however, the conical collared component group was significantly more stable than the collarless control group in transverse (primarily rotational) micromotion. The overall average measured transverse motion for the collarless control group was more than 3.7 times greater than that of the conical collar group at scaled stair-climbing loads. The two conical collared components loaded to full peak stair-climbing load (2,100 N) exhibited micromotion under 160 microns. The results suggest that the conical collar may improve stability of an uncemented prosthesis under loads that include an out-of-plane (rotational) component.

    View details for PubMedID 1431921



    We studied the acquisition of bone mineral in 45 healthy prepubertal and pubertal girls and related changes in bone mass to age, body mass, pubertal status, calcium intake, and exercise. A subgroup of 12 girls was followed longitudinally. Bone mineral content (BMC) of the lumbar spine, whole body, and femoral neck was measured by dual energy x-ray absorptiometry and that at the midradius by single photon absorptiometry. For comparison, spine and whole body mineral contents were also measured by dual photon absorptiometry. Bone mass was expressed in conventional terms of BMC and area density (BMD). However, we show that BMD fails to account for differences in bone thickness. Since bone size increases during adolescence, we present a new expression, bone mineral apparent density (BMAD), which is BMC normalized to a derived bone reference volume. This term minimizes the effect of bone geometry and allows comparisons of mineral status among bones of similar shape but different size. BMC increased with age at all sites. These increases were most rapid in the early teens and plateaued after 16 yr of age. When bone mineral values at all sites were regressed against age, height, weight, or pubertal stage, consistent relationships emerged, in which BMC was most strongly correlated, BMD was correlated to an intermediate degree, and BMAD correlated only modestly or without significance. Dietary calcium and exercise level did not correlate significantly with bone mass. From these relationships, we attribute 50% of the pubertal increase in spine mineral and 99% of the change in whole body mineral to bone expansion rather than to an increase in bone mineral per unit volume. In multiple regressions, pubertal stage most consistently predicted mineral status. This study emphasizes the importance of pubertal development and body size as determinants of bone acquisition in girls. BMAD may prove to be particularly useful in studies of bone acquisition during periods of rapid skeletal growth.

    View details for Web of Science ID A1991GW87900028

    View details for PubMedID 1955516



    Conventional stereologic methods for expressing the orientation of anisotropic materials are limited to materials assumed to possess orthogonal directions of orientation. In many substances, including cancellous bone, this assumption is unsubstantiated. Presented here are two simple methods for characterizing the orientation of any anisotropic material within a plane. By modeling the substance as a series of lines oriented in particular directions, it is possible to arrive at either a "phase distribution" that expresses the degree of orientation distributed over a range of angles or a series of "primary orientations" that express the degree of orientation at a select number of angles, with an additional measure of the degree of isotropy. This characterization of anisotropy is highly dependent on such parameters as feature size, sample size, test line spacing, and test line width. Given the careful selection of these parameters, the new methods provide simple measures of orientation, which may prove useful in testing Wolff's trajectorial theory of the relationship between mechanical stresses and the orientation of cancellous bone.

    View details for Web of Science ID A1991GL04300018

    View details for PubMedID 1919856



    We used a voluntary running model to explore the relationship between average daily running distance and bone mineral status of rats. A total of 60 male Sprague-Dawley rats were randomly assigned at 6 weeks of age to a sedentary control group (n = 22) or to a group with unlimited access to a running wheel (n = 38). The running distance of exercising rats was monitored daily, and steady-state running levels ranged from 3.2 to 18.1 km/day. At the end of the experimental period, femora and tibiae were dissected and bone mineral content (BMC, g/cm) and bone mineral density (BMD, g/cm2) were measured by single-photon absorptiometry. Cross-sectional morphometry was examined by taking a transverse section of the femoral middiaphysis. Hindlimb percentage fat was significantly higher in controls than in runners (20.0 +/- 1.2 versus 11.1 +/- 0.6, p less than 0.001), and soleus mass was greater in runners than in controls (371 +/- 8.1 versus 320 +/- 0.8 mg, p less than 0.001). Femoral and tibial lengths, weights, and volumes were significantly higher in runners than in controls (p less than 0.005). BMC and BMD were higher in runners than in controls at all sites apart from the distal femur. Cross-sectional areas at the femoral midshaft were greater in running rats than in sedentary controls (6.26 +/- 0.1 versus 5.45 +/- 0.3 mm2, p less than 0.02), as was the polar moment of inertia (15.6 +/- 0.6 versus 12.7 +/- 0.2 mm4, p less than 0.05). No positive correlation was found between distance run and BMC, BMD, cross-sectional area, or polar moment of inertia.(ABSTRACT TRUNCATED AT 250 WORDS)

    View details for Web of Science ID A1991GN78500010

    View details for PubMedID 2035355



    The variety of fixation peg designs existing on prosthetic implants indicates uncertainty regarding the optimum design of fixation pegs for the reduction of stress and relative motion at the bone-implant interface. Fixation pegs have a number of important functions on a prosthesis, one of which is to reduce shear stress and shear displacement at the bone-implant interface. This is a parametric study intended to identify trends in the shear stability of prostheses incorporating a range of fixation peg designs. The parameters varied included the number of fixation pegs on a surface, the size of the pegs, and the aspect ratio (length/diameter) of the pegs. Mechanical tests were performed on urethane foam blocks with mechanical properties comparable to trabecular bone. The results indicated the following: (a) Fixation pegs act independently in resisting shearing force if they are spaced sufficiently far apart. (b) For any given shear displacement, smaller pegs generate a greater resistive shear force per unit of peg projected area in the direction of the applied load than larger pegs having the same aspect ratio. (c) Smaller diameter pegs cause the supporting material to yield at lower displacements. (d) Pegs with a high aspect ratio provide high shear stability with a minimum amount of bone removed, but may bend if the aspect ratio becomes excessive. (e) Smaller, slender pegs generate a greater resistive shear force at a given displacement per unit of peg volume than larger, lower aspect ratio pegs.(ABSTRACT TRUNCATED AT 250 WORDS)

    View details for Web of Science ID A1990EF13000014

    View details for PubMedID 2213346



    A time-dependent approach for emulating bone modeling and remodeling in response to the daily loading history is presented. We postulate that genotype, systemic metabolic conditions, and local tissue interactions establish the level of local tissue mechanical stimulation (attractor state) appropriate for the maintenance of bone tissue. The net daily rate of apposition or resorption on a bone surface is determined by the difference between the actual stimulus and the tissue attractor state and can be modulated by other biologic factors. In calculating the net change in local bone apparent density, the technique takes into account the bone surface area available for osteoblastic and osteoclastic activity. Endosteal, periosteal, haversian, and cancellous bone modeling and remodeling are thereby treated in a consistent, unified fashion.

    View details for Web of Science ID A1990DU81900005

    View details for PubMedID 2388105

  • Effects of fluoride treatment on bone strength. Journal of bone and mineral research Carter, D. R., Beaupré, G. S. 1990; 5: S177-84


    Bone mass and architecture in appendicular and most axial sites is controlled primarily by the tissue-loading history. We introduce a conceptual framework for understanding how fluoride treatment alters this control and can cause systemic increases in bone mass. Due to possible adverse influences of fluoride on the mineralized tissue physical characteristics, however, the increase in bone mass does not necessarily result in an increase in bone strength. Using engineering analyses of bone trabeculae, we calculate the losses in trabecular strength which can be caused by the presence of hypomineralized or hypermineralized fluorotic tissue. Significant increases in bone volume fraction and bone mass may be required to overcome these strength deficits.

    View details for PubMedID 2187326



    In a series of in vitro organ culture experiments by Klein-Nulend et al., intermittent ambient hydrostatic pressure was found to significantly increase the rate of calcification in the diaphysis of mouse rudiments while proteoglycan production was increased in the noncalcified epiphyses. In this study, we have conducted finite element stress analyses of this organ culture system in an effort to better understand the distribution of local tissue stresses which were created. Furthermore, we sought to clarify how these experimental results relate to our theory for skeletal morphogenesis which postulates that endochondral ossification is accelerated in regions of octahedral shear (deviatoric) stress and inhibited in areas of compressive hydrostatic (dilatational) stress. The results of the stress analyses show that externally applied hydrostatic pressure produces significant shear stresses at the cartilage/calcified cartilage interface and pure hydrostatic pressure at the rudiment ends. The accelerated osteogenesis in regions of high shear and the increased synthesis of proteoglycans in regions of high compressive hydrostatic stress are therefore consistent with our theory which predicts the regulation of cartilage maintenance and endochrondral ossification by intermittent tissue stresses.

    View details for Web of Science ID A1990DA96200009

    View details for PubMedID 2357423



    The role of mechanical stresses in the formation of endochondral ossification patterns and the construction of basic bone architecture in human long bones is investigated using a three-dimensional generalized model of long bone development. The distribution of mechanical stress which is created in developing bones as a result of intermittent mechanical loading is calculated using a computer model that mathematically represents the bone's geometry, material properties and loading conditions. The process of endochondral ossification is simulated by iteratively converting cartilaginous regions of the computer model to bone, based on the calculated intermittent hydrostatic and shear stress distributions. Once local regions of mineralized bone have formed, these regions are remodeled according to an algorithm which relates bone density to a mechanical stress stimulus. The results simulated the correct sequence of the appearance of morphological structures which are common to long bones in the human appendicular skeleton. These developmental structures include the site of the first endochondral bone and the secondary ossification center and the tubular nature of long bones. Our results suggest that mechanical loading histories may influence bone morphogenesis beginning from the early stages of endochondral ossification and continuing throughout life. The stress-based algorithms may be part of the 'rules of construction' or 'developmental constraints' which guide limb ontogeny.

    View details for Web of Science ID A1990DN83800002

    View details for PubMedID 2396753



    A new theory relating bone morphology to applied stress is used to predict the apparent density distribution in the femoral head and neck. Cancellous bone is modeled as a self-optimizing material and cortical bone as a saturated (maximum possible bone density) response to stress in the bone tissue. Three different approaches are implemented relating bone apparent density to: (1) the von Mises stress, (2) the strain energy density in the mineralized tissue and (3) a defined closed effective stress (spherical stress). An iterative nonlinear three-dimensional finite element model is used to predict the apparent density distribution in the femoral head and neck for each of the three approaches. It is shown that the von Mises stress (an open effective stress) cannot accurately predict bone apparent density. It is shown that strain energy density and the defined closed effective stress can predict apparent density and that they give predictions consistent with the observed density pattern in the femoral head and neck.

    View details for Web of Science ID A1990CQ50200001

    View details for PubMedID 2307686



    The progressive ossification pattern in a fracture callus was predicted based on a theory that relates the local stimulus for ossification to the tissue mechanical loading history. Two-dimensional finite element analyses of a fracture callus were considered at three different stages of ossification. The sites of callus ossification represented in the initial model were predicted by previous analyses relating mechanical stress and vascularity to the differentiation of mesenchymal tissue in the early callus. The zones of further ossification, bone bridging, and bone consolidation predicted in the present study were found to be similar to the ossification patterns that have been documented by other researchers. The approach used to predict fracture healing is identical to that of previous studies predicting joint morphogenesis, with the exception that fracture healing requires continuous, attached skeletal elements, whereas joint morphogenesis requires discontinuous, articulating skeletal elements.

    View details for Web of Science ID A1989U311000011

    View details for PubMedID 2703931



    Most long bone fractures are the result of bending and/or torsional loading. To allometrically relate bone torsional and bending strength to animal mass (M), we define the bone strength index SB = J/dl where J = midshaft cross section polar moment of inertia, d = diameter, and l = length. In geometrically similar scaling, one would expect SB alpha M2/3. In this study, long bone geometric parameters were measured for 12 species of Artiodactyls. The relationships determined for length and diameter are similar to those reported by previous investigators (l alpha d3/4, l alpha M1/4). For the Artiodactyls studied, we found that SB alpha M0.82. Data previously collected by Biewener on a wide range of mammals (non-Artiodactyls) showed different scaling characteristics (l alpha d0.89, l alpha M0.31). However, our analysis of his data suggests roughly similar scaling of the torsional and bending strength index, SB alpha M0.77. It therefore appears that, in spite of differences in scaling of length and external diameter, the bending and torsional strengths scale similarly across a broad range of animals.

    View details for Web of Science ID A1989CN19300007

    View details for PubMedID 2625417



    A theory relating bone maintenance to mechanical loading history has been applied to successfully predict the distribution of bone density and trabecular orientation in the adult proximal femur. The loading history was simulated by determining the stress fields in a two-dimensional finite element model exposed to various discrete loading cases and making assumptions about the relative number of loading cycles associated with each load case. The total stimulus to bone maintenance was then calculated by a linear superposition of the stimulus of each loading case. Based on the calculated total stimulus, the apparent density and material properties of each element were changed and the stress solutions were again determined. Using this iterative technique, the bone apparent density and orientation characteristics were predicted. The results indicate that the trabecular morphology of the femur can only be explained by considering the joint loadings from multiple directions. Contrary to the 'trajectorial theory' promoted by Wolff (The Law of Bone Remodelling, 1892), trabecular orientations predicted from our multiple-load analyses are not necessarily perpendicular and do not correspond to the principal stress directions of any one loading condition. Our predicted orientations correspond better to the drawing of bone trabecular morphology by von Meyer (Archs Anat. Physiol. wiss. Med. 34, 615-628, 1867) than to the classic drawing by Wolff and suggest that further study of the trajectorial theory is warranted.

    View details for Web of Science ID A1989U216000005

    View details for PubMedID 2722894



    Creep and fatigue tests were performed on human femoral cortical bone and the results were compared to a cumulative damage model for bone fracture. Fatigue tests in tension, compression, and reversed loading with a tensile mean stress were conducted at 2 Hz and 0.02 Hz. Load frequency had a strong influence on the number of cycles to failure but did not influence the total time to failure. Bone displayed poor creep-fracture properties in both tension and compression. The fracture surfaces of the tensile creep specimens are distinctly different than those of the compressive specimens. The results suggest that tensile cyclic loading creates primarily time-dependent damage and compressive cyclic loading creates primarily cycle-dependent damage. However, data for load histories involving both tensile and compressive loading indicate lower time to failure than predicted by a simple summation of time-dependent and cycle-dependent damage.

    View details for Web of Science ID A1989CA09200013

    View details for PubMedID 2808445



    The possible role of mechanical loading history in chondroosseous development at the ends of long bones is explored using two-dimensional finite element models of chondroepiphyses. Loading histories are characterized in terms of discrete loading cases defined by joint contact pressure distributions and an associated number of loading cycles. An osteogenic stimulus throughout the chondroepiphyses is calculated following the theory that cyclic octahedral shear stresses promote endochondral ossification and cyclic compressive dilatational stresses inhibit ossification. The resulting distributions for the osteogenic stimulus predict the appearance of the secondary ossific nucleus and the shape of the developing bony epiphysis. The zone of Ranvier and the formation of articular cartilage and the growth plate are also predicted by the models. These findings are consistent with the hypothesis that tissue stress histories constitute an important influence during skeletal morphogenesis. Further study and testing of the concepts introduced in this study are appropriate.

    View details for Web of Science ID A1988Q630400003

    View details for PubMedID 3171761



    A general theory for the role of intermittently imposed stresses in the differentiation of mesenchymal tissue is presented and then applied to the process of fracture healing. Two-dimensional finite element models of a healing osteotomy in a long bone were generated and the stress distributions were calculated throughout the early callus tissue under various loading conditions. These calculations were used in formulating theoretical predictions of tissue differentiation that were consistent with the biochemical and morphological observations of previous investigators. The results suggest that intermittent hydrostatic (dilatational) stresses may play an important role in influencing revascularization and tissue differentiation and determining the morphological patterns of initial fracture healing.

    View details for Web of Science ID A1988P849300016

    View details for PubMedID 3404331



    The use of an internal fixation plate in the presence of a bone defect was studied using a theoretical model of an idealized long bone having a circular cross section and loaded using a combination of axial and bending loads. The analysis showed that the "bending-open" loading mode does not occur if, in the normal unplated bone, the line of action of the resultant axial load passes within the outer cortex at the location where the plate is to be applied. In this situation the fracture will deform in a "bending-closed" mode regardless of whether the plate is attached to the tension or the compression side. If bony contact cannot be achieved, lower plate stress is always encountered when the plate is attached to the compression side instead of the tension side. In vivo verification of the model was addressed in a pilot experiment using instrumented metal plates applied bilaterally to the femora of one dog. Bilateral bone defects were created in the midfemoral canine diaphysis. On one leg the plate was applied to the lateral aspect ("tension" side), and on the other leg the plate was applied to the medial aspect ("compression" side). The plate attached to the lateral aspect deformed plastically in the bending-closed mode. The contralateral plate that was attached to the medial aspect (compression side) of the femur did not show signs of plastic deformation. Furthermore, the plate strains were lower in the plate attached to the medial aspect than those in the plate attached to the lateral aspect.(ABSTRACT TRUNCATED AT 250 WORDS)

    View details for Web of Science ID A1988P849300014

    View details for PubMedID 3404329



    Metal backing of glenoid components for total shoulder replacements and the use of bony ingrowth surfaces on these components have recently been introduced. In this study, finite element analyses were performed to determine the stress fields in the natural glenoid and to calculate the change in bone stresses after implantation of glenoid components of various designs. The effects of metal backing, keel geometry, and superior constraint on bone stresses indicate that stress distributions on the natural glenoid corresponded to bone morphology. Metal-backing the glenoid component may cause slight improvement in stress transfer to cortical bone. Altered fin geometry better stabilized the glenoid component. Superior restraints on the component intending to prevent subluxation increase stresses and may cause earlier loosening than encountered with unconstrained components.

    View details for Web of Science ID A1988P023100029

    View details for PubMedID 3383490



    Three different interface geometries for porous ingrowth surface replacements of the hip were examined using two-dimensional linear and nonlinear contact finite element analyses. The results indicate that incorporation of a nearly flat prosthesis interface between the surface replacement and the underlying cancellous bone may reduce stress shielding and improve stress transfer from the component. For all designs analyzed, the bone stress shielding was insensitive to component material stiffness when the elastic modulus was greater than 30 MPa. The use of titanium instead of cobalt-chrome (Co--Cr) as the prosthesis material therefore had a negligible effect on stress shielding.

    View details for Web of Science ID A1988N110300013

    View details for PubMedID 3357091



    Using a three-dimensional finite element model of a plated long bone, we studied the influence of screw tightness, sliding frictional interfaces, and loading magnitude on the stresses within the plated bone. The model incorporated frictional interface elements that allowed stress-free separation under tensile loading to occur between the plate and bone and between the screw heads and the plate. The applied loading stimulated both static preloads created by tightening the screws that secure the plate to the bone and physiologic loads created by activity. Initial screw tightening with plate application created regions of bone hydrostatic compressive stress that may be partly responsible for ischemia under the plate. The inclusion of frictional interfaces resulted in a nonlinear relationship between physiologic loan and bone strain that was dependent on screw tightness. This nonlinear response correlated well with the results of previous in vitro studies showing that slippage between the plate and the bone can occur at physiologic load levels. The results showed that the effect of such slippage can be at least as important as plate material, rigidity, and placement in determining the degree of stress shielding. The results also indicated that previous plated bone models that assumed tight interfaces may have overestimated the extent of mechanical stress shielding.

    View details for Web of Science ID A1988L307200005

    View details for PubMedID 3334738



    Using a mathematical model which relates bone density to daily stress histories, the influence of physical activities on the apparent density of the calcaneal cancellous bone was investigated. Assuming that the mechanical bone maintenance stimulus is constant for all bone tissue, bone apparent density was calculated by a linear superposition of the mechanical stimulus provided by different daily physical activities. An empirical weighting factor, m, accounted for possible differences in the relative importance of load magnitude and number of cycles in each activity. By considering hypothetical variations in body weight and occupational activity levels, the range of probable m values was established. The model was then applied to the results of two previous running studies in which calcaneal density was measured to obtain an estimate of the stress exponent parameter, m. The results indicate that stress magnitudes (or joint forces) have a greater influence on bone mass than the number of loading cycles. We demonstrate that by carefully considering the magnitudes of imposed skeletal forces and the number of loading cycles, it may be possible to design exercise programs to achieve predictable changes in bone mass.

    View details for Web of Science ID A1988Q581200005

    View details for PubMedID 3225269



    We calculated subchondral deformations and stresses in the femoral head and acetabulum during weight bearing using finite element models. Areas of high joint contact pressures on the femoral head were shown to correspond to high hydrostatic compression in subchondral bone. The magnitude of the subchondral bone compressive hydrostatic stress correlated with cartilage thickness and was highest in the superior femoral head and moderate at the acetabular roof. The seldom contacting surfaces of the medial-inferior and peripheral areas of the femoral head and the roof of the acetabulum had lower hydrostatic compression and significant subchondral bone tensile strains tangential to the joint surface. Initial cartilage fibrillation and osteophyte formation are often found in these areas. These findings suggest that fluctuating hydrostatic pressure inhibits vascular invasion and the degeneration and ossification of articular cartilage. The generation of tensile strain may promote the degenerative process by direct mechanical mechanisms. Additionally, since tensile strains are associated with a reduction in the compressive hydrostatic stresses in the cartilage and an increase in shear stresses, their presence may permit or promote vascular invasion, cartilage degeneration, and osteophyte formation. These mechanical principles in arthrosis are the same as those that have been previously demonstrated to guide the degeneration and ossification of the cartilage primordium during skeletal morphogenesis. In this sense, arthrosis may be viewed as the final stage in the degeneration and ossification of the cartilage anlage.

    View details for Web of Science ID A1987M477800002

    View details for PubMedID 3442205



    A new theory is introduced to describe some of the influences of mechanical stresses on chondroosseous biology. It is proposed that degeneration and ossification is a normal process for all cartilage in the appendicular skeleton, which is accelerated by intermittently applied shear stresses (or strain energy), and inhibited or prevented by intermittently applied hydrostatic pressure. These concepts were applied using finite element computer models in an effort to predict the ossification pattern of the prenatal and postnatal femoral anlage. The theoretical calculations successfully predicted the key features of skeletal morphogenesis including the development of the primary ossification site, a tubular diaphysis and marrow cavity, metaphyseal and epiphyseal trabecular bone, the location and geometry of the growth plate, the appearance and location of the secondary ossific nucleus, and the existence and thickness distribution of articular cartilage. The results suggest that degenerative joint disease in immobilized or nonload-bearing mature joints may be a manifestation of the final stage in the ossification of the anlage. In nonfunctional joints, the absence or reduction of intermittent hydrostatic pressure in the articular cartilage permits cartilage degeneration and the progressive advance of the ossification front toward the joint surface until the articular cartilage has been ossified.

    View details for Web of Science ID A1987H634700034

    View details for PubMedID 3581576

  • Acetabular lucent lines and mechanical stress in total hip arthroplasty. journal of arthroplasty Goodman, S. B., Carter, D. R. 1987; 2 (3): 219-224


    The radiographs of 97 patients (117 hips) who had a straight-stem Muller femoral component and a non-metal-backed acetabular component were reviewed to determine whether the mode of acetabular loosening predicted by finite element stress analysis (FESA) is observed clinically. The follow-up period averaged 3.1 years (range, 2.0-4.6 years). Significantly more lucent lines were present in zones 1 and 3, compared with zone 2 (P less than .01). This finding corroborates the predictions of FESA and suggests that the production of acetabular lucent lines is due in part to chronic mechanical overload.

    View details for PubMedID 3668551



    Two-dimensional linear and contact finite element analyses were conducted of total hip arthroplasty using metal-backed, porous ingrowth acetabular components. The stress transmission characteristics from the component to the surrounding bone were given special attention. Resultant loads of 20 and 40 degrees medial of vertical were studied, and the influence of adding a metal flange to the rim of the cup was evaluated. The results indicated that when a conventional metal-backed component (without a flange) is initially implanted and subjected to normal loading, these components may experience distraction between the component and the surrounding bone at inferior sites. Compressive stresses in the superior dome cancellous bone, however, will be substantial. If complete porous ingrowth is achieved, the superior dome compressive stresses will be reduced and substantial shear stresses created. In addition, high local bone stresses were found at the component rim. If bone ingrowth is achieved only in specific locations, stress transmission will be dictated by those locations and may differ markedly from the case of complete bone ingrowth. In the event that no porous ingrowth is achieved and a fibrous layer forms around the component, the interface stresses will be similar to those calculated for the natural hip. The addition of a flange to the rim of the cup will reduce the magnitude of the radial stresses transmitted to the cancellous bone superiorly and medially by directly transferring some of the load to the lateral wall of the pelvis. The flange will also help to relieve the high local stresses that are found at the component rim.

    View details for Web of Science ID A1987L138700009

    View details for PubMedID 3681529



    A comprehensive theory which relates tissue mechanical stresses to many features of skeletal morphogenesis, growth, regeneration, maintenance and degeneration is reviewed. The theory considers the repeated or intermittent mechanical forces which constitute the loading history on the chondro-osseous skeleton. The results of numerous mechanical stress analyses indicate that the local tissue stress history plays a major role in controlling connective tissue biology. The strong influence of mechanical energy in ontogenesis implies a comparably strong influence in phylogenesis. The fact that the mechanical stress histories in skeletal tissues are directly related to the force of gravity suggests that the life forms that have evolved on Earth are closely tied to our gravitational field.

    View details for Web of Science ID A1987L506100010

    View details for PubMedID 3323201



    The method of considering a single loading condition in the study of stress/morphology relationships in trabecular bone is expanded to include the multiple loading conditions experienced by bone in vivo. The bone daily loading histories are characterized in terms of stress magnitudes or cyclic strain energy density and the number of loading cycles. Relationships between local bone apparent density and loading history are developed which assume that bone mass is adjusted in response to strength or energy considerations. Three different bone maintenance criteria are described which are formulated based upon: (1) continuum model effective stress, (2) continuum model fatigue damage accumulation density, and (3) bone tissue strain energy density. These approaches can be applied to predict variations in apparent density within bone and among bones. We show that all three criteria have similar mathematical forms and may be related to the density (or concentration) of bone strain energy which is transferred (dissipated) in the mineralized tissue. The loading history and energy transfer concepts developed here can be applied to many different situations of growth, functional adaptation, injury, and aging of connective tissues.

    View details for Web of Science ID A1987J837300007

    View details for PubMedID 3654678



    The relationships between cancellous bone apparent density, trabecular orientation, and stress are developed and a mathematical theory describing these relationships is proposed. The bone is assumed to be a self-optimizing material. Using a continuum model, sufficient conditions are developed which ensure that, for a given stress encountered during normal activity, the theory will predict both trabecular orientation and apparent density. Using two special approaches, one based on optimizing strain energy density (stiffness) and the other on optimizing strength, the relationship between apparent density and stress is derived. This is the first time that a single theory has been advanced to predict both the orientation and apparent density of cancellous bone.

    View details for Web of Science ID A1986D614100007

    View details for PubMedID 3734938



    A two-dimensional, finite element study was undertaken to establish the stresses in the proximal tibia before and after total knee arthroplasty. Equivalent-thickness models in a sagittal plane were created for the natural, proximal tibia and for the proximal tibia with two different types of tibial plateau components. All components simulated bony ingrowth fixation, i.e. no cement layer existed between component and bone. In addition, the interface between component and bone was assumed to be intimately connected, representing complete bony ingrowth and a rigid state of fixation. Two load cases were considered: a joint reaction force acting in conjunction with a patellar ligament force, simulating the knee at 40 degrees of flexion; and a joint reaction force directed along the long axis of the tibia. For the natural tibia model, the pattern of principal stresses for loadcase 1 more closely corresponds to the epiphyseal plate geometry and trabecular morphology than do the principal stress patterns for loadcase 2. Judging from the distribution of principal stresses, loadcase 1 represents a more severe test of implant design than does loadcase 2. The model of the component with a peg predicted that the trabecular bone near the tip of the peg will experience higher than normal stresses, while the bone stresses near the posterior aspect adjacent to the metal tray will be reduced. A component without pegs that incorporates a posterior chamfer and an anterior lip lead to stress distributions closer to those existing in the natural tibia. The interface geometry for this design is based upon the contour of the epiphyseal plate.

    View details for Web of Science ID A1986D987400010

    View details for PubMedID 3771588



    Geometric, elastic, and structural properties of growing rat femora were determined from bending and torsion tests followed by bone sectioning and measurement of areal properties. Rosette strain gages bonded to the bone surface measured the strain during testing. A computer generated elliptical cross-sectional representation of the cross section geometry was used for calculation of material and structural properties. All structural and material properties increased with increasing age, exhibiting age-related changes that were best represented by an allometric or "heterauxic" growth pattern (y = axb) up to maturity. The femoral axial, flexural, and torsional rigidity increased 5.7, 10.1, and 14.8 fold, respectively, during maturation from 21 to 119 days of age. The increase in whole bone rigidity during maturation was caused primarily by changes in geometry. The bone tissue tensile longitudinal elastic modulus and shear modulus approximately doubled, and the shear strength increased approximately fourfold over this same period. Following maturity, a much slower increase in bending and torsional properties was noted. The results suggest that bone structural properties are regulated by changes in both geometric and material properties.

    View details for Web of Science ID A1986A508600007

    View details for PubMedID 3950809



    Two-dimensional, finite element studies were conducted of the proximal tibia before and after joint arthroplasty. Equivalent-thickness models projected onto the mid-frontal plane were created for the natural, proximal tibia and for the proximal tibia with four different types of tibial plateau components. All components simulated bony ingrowth fixation, i.e. no cement layer existed between component and bone. In addition, the interface between component and bone was assumed to be intimately connected, representing complete bony ingrowth and a rigid state of fixation. Loads consisted of bi-condylar and uni-condylar forces. Results indicated that conventional plateau designs with central posts or multiple pegs led to higher stress magnitudes in the trabecular bone near the distal ends of the post/pegs and stress shielding at more proximal locations. A design without posts or pegs whose interface geometry mimics the epiphyseal plate minimizes bone stress shielding. An implant consisting of separate components covering each condyle was found effective in limiting component tilting and the consequent tensile stresses caused by non-symmetrical, uni-condylar loading.

    View details for Web of Science ID A1986D987400009

    View details for PubMedID 3771587



    Two-dimensional finite element analyses were conducted of the normal hip using contact elements at the joint surface. The models studied were constructed for a slice through the pubis, acetabulum, and ilium. In the analyses the proximal femur was pressed into the acetabulum and intraarticular pressures and principal stresses in the joint region were determined for different load magnitudes and directions and various boundary conditions. Three sets of boundary conditions were examined: (a) deformable pubic symphysis, (b) rigid pubic symphysis, and (c) simulations of experimental studies. In the deformable model the pubic symphysis was free to displace in the sagittal plane and rotate. In the rigid model the pubic symphysis was rigidly fixed. Superoposterior loading resulted in high-contact pressures at the acetabular dome for all sets of boundary conditions. For the deformable model subject to a more medially directed load the acetabulum closed in such a manner as to squeeze the head of the femur creating high-contact pressures superiorly and inferiorly. This resulted in significant compressive stresses in the superior dome cancellous bone and inferior cancellous bone. The cumulative effect of this squeezing action with normal biological remodeling may cause elongation of the femoral head resulting in asphericity and incongruity of the unloaded hip joint articular surfaces. Rigidly fixing the pubic symphysis stiffened the model and resulted in principal stress patterns that did not reflect trabecular density or orientations as well as those of the deformable pubic symphysis model. Finite element simulations of previous experimental studies modeled the close proximity of the fixation to the excised acetabulum. These boundary conditions prevented the squeezing caused by pelvis deformations. The resulting contact areas, pressure distributions, and bone stresses were very different from those of the more anatomic, deformable pubic symphysis model. These findings demonstrate the sensitivity of hip contact pressures and stresses to imposed boundary conditions and indicate that care should be taken to simulate anatomic conditions in experimental and theoretical studies.

    View details for Web of Science ID A1985AVS0700006

    View details for PubMedID 4067702



    A mathematical model is presented to describe the combined time-dependent and cycle-dependent fracture characteristics of devitalized cortical bone. Failure is interpreted based on a linear-life fraction rule, which accounts for cumulative creep and fatigue damage under arbitrary loading histories. The model is successful in describing the influence of loading rate on monotonic tensile strength, the time to failure in constant stress creep-fracture tests, and bone fracture in zero-tension and tension-compression cyclic loading. The possible implications of the model to in vivo bone fracture, deformity, and remodelling in response to various loading histories are considered.

    View details for Web of Science ID A1985ALR9100010

    View details for PubMedID 3981298



    Two different dual-energy projection radiography techniques were utilized in an attempt to predict femoral neck strength, bone density, and bone mineral content in 19 pairs of cadaver specimens. Positive simple linear correlation was observed between dual-energy scanned projection measurements and dry density, ash fraction, cross-sectional cortical bone area and, to a lesser degree, force required for fracture, but not trabecular bone volume, failure time, or Singh trabecular grade. Dual-energy film radiography was found to be a less reliable indicator of femoral neck strength, density, and mineral content. Dual-energy scanned projection results related linearly to mineral-equivalent solution (K2HPO4) concentration, and demonstrated long-term reproducibility in repeated specimen studies. Correction factors derived to account for differences in femoral size and rotation were shown to be reliable over a moderate range of neck projections. Although bone mineral measurement at other sites may provide comparable or greater information concerning hip fracture risk, dual-energy scanned projection radiography appears to be a useful technique for assessment of bone density, mineral content, and strength in the femoral neck.

    View details for Web of Science ID A1985ANR0300007

    View details for PubMedID 4044193

  • FATIGUE OF IMMATURE BABOON CORTICAL BONE JOURNAL OF BIOMECHANICS Keller, T. S., LOVIN, J. D., Spengler, D. M., Carter, D. R. 1985; 18 (4): 297-304


    Strain-controlled uniaxial fatigue and monotonic tensile tests were conducted on turned femoral cortical bone specimens obtained from baboons at various ages of maturity. Fatigue loading produced a progressive loss in stiffness and an increase in hysteresis prior to failure, indicating that immature primate cortical bone responds to repeated loading in a fashion similar to that previously observed for adult human cortical bone. Bone fatigue resistance under this strain controlled testing decreased during maturation. Maturation was also associated with an increase in bone dry density, ash fraction and elastic modulus. The higher elastic modulus of more mature bone meant that these specimens were subjected to higher stress levels during testing than more immature bone specimens. Anatomical regions along the femoral shaft exhibited differences in strength and fatigue resistance.

    View details for Web of Science ID A1985AKC4600006

    View details for PubMedID 4019527



    Finite element stress analyses were performed on the proximal humerus before and after the simulated implantation of stemmed, metallic prosthetic components with porous sintered surfaces for direct bony attachment. Design geometries with surfaces at the prosthetic head/bone interface that were (a) convex, (b) flat, and (c) concave were studied. Analyses for each of the three geometries were conducted to reflect (a) bone ingrowth on all the prosthesis/bone surfaces and (b) bone ingrowth only along the underside of the prosthetic humeral head (assuming the stem was not coated with a porous material). Three loading conditions were used to model various degrees of abduction of the arm. Results indicated that in the normal humerus the compressive joint forces are transmitted from the articular surface through cancellous bone to the inferior cortical shell. Contraction of the rotator cuff muscles created tensile stresses in the superolateral cancellous bone and the superior cortical shell of the humerus. Results of the implanted humeral component models indicated that the use of a prosthesis with bone ingrowth along the stem would cause marked stress shielding proximally whereas the use of implants with porous ingrowth only on the underside of the humeral head replacement produced stress fields more similar to the normal humerus. The convex, flat, and concave surfaces provided similar load transfer from the component to the underlying bone in all loading cases. Other prosthetic head designs that may offer better initial stability produced stress fields similar to those of existing prostheses.

    View details for Web of Science ID A1985ARV6600013

    View details for PubMedID 4032107



    The influences of heterogeneity, anisotropy and geometric irregularity on the unrestrained, linearly elastic torsional response of long bones are assessed. Longitudinal geometric variations contribute insignificantly to the torsional response for typical long bone geometries. Anisotropy, heterogeneity and transverse geometric irregularity significantly influence the torsional response. A procedure is discussed which uses an approximate means to characterize both heterogeneity and anisotropy in predicting the torsional response. The accuracy of circular and elliptical annulus models of the bone cross-sectional geometry are assessed by comparing the stress predictions of these simple models to those of finite element models of the bone geometry.

    View details for Web of Science ID A1985AHW4000013

    View details for PubMedID 3999715



    Finite element stress analyses were conducted of the canine femoral head before and after implantation of various surface replacement-type components. The femoral head was replaced by four implant geometries; (a) shell, (b) shell with peg, (c) shell with rod, and (d) a new epiphyseal replacement design. All implants were modelled to simulate bony ingrowth along the underside of the shell and along the surfaces of the peg and rod. The results indicated that in the normal femur the forces are transferred from the articular surface through the femoral head cancellous bone to the inferior cortical shell of the femoral neck. After shell-type surface replacement, forces were transferred more distally at the rim of the shell and at the end of the peg or rod, thereby reducing the stresses in the proximal head cancellous bone. Computer simulation of bone remodelling due to proximal bone stress reduction was shown to accentuate the abnormality of the stress fields. Surface replacement with a lower modulus material created a less abnormal redistribution of bone stresses. The new epiphyseal replacement design resulted in stress distributions similar to those in the normal femoral head and minimal shear stresses at the implant/bone interface. These findings suggest that the epiphyseal replacement concept may provide better initial mechanical integrity and create a more benign milieu for adaptive bone remodelling than conventional, shell-type surface replacement components.

    View details for Web of Science ID A1984TT66300004

    View details for PubMedID 6526832



    A conceptual framework is presented for understanding and investigating structural adaptation of cortical bone. The magnitudes, orientations, and sense (tension or compression) of the physiologically incurred cyclic principal strains vary markedly throughout the skeleton. It is probable, therefore, that the strain/remodeling response of bone is site specific. Furthermore, there is some indication that immature bone is more responsive to alterations of cyclic strains than mature bone. Animal experimental studies and complementary stress and strain analyses suggest that the structural adaptation due to changes in cyclic strain fields may be a very nonlinear response. Bone loss in mature animals due to immobilization is sensitive to even small changes in the cyclic bone strains. Under normal conditions, however, there appears to be a broad range of physical activity in which bone is relatively unresponsive to changes in loading history. With severe repeated loading, bone hypertrophy can be pronounced. These observations open the possibility that bone atrophy and hypertrophy are controlled by different mechanisms. Therefore, two (or more) complementary control systems may be involved in the regulation of bone mass by bone cyclic strain histories. It is probable that bone mechanical microdamage is one control stimulus for affecting an increase in bone mass.

    View details for Web of Science ID A1984TB16000004

    View details for PubMedID 6430518



    Fatigue tests of human cortical bone (up to 1.74 X 10(6) cycles) were conducted under tension-compression (T-C) and zero-tension (O-T) modes with a 2Hz, stress controlled, sinusoidal loading history. Tensile creep-fracture tests at constant stress levels were also performed. The relationship between the initial cyclic strain range and cycles to failure with the T-C specimens were consistent with that derived previously in low-cycle fatigue under strain control. Using a time-dependent failure model, the creep-fracture data was found to be consistent with previous studies of the influence of strain rate on the monotonic tensile strength of bone. The model also predicted quite well the time to failure for the O-T fatigue specimens, suggesting that creep damage plays an important role in O-T fatigue specimens.

    View details for Web of Science ID A1983QV85400010

    View details for PubMedID 6865359



    Tensile fatigue tests of acrylic bone cement were conducted under strain control in a wet environment at 37 degrees C. A constant strain rate of 0.02s-1 was used, resulting in physiologic loading frequencies. Comparison of the tensile fatigue data with the results of previous tension-compression fatigue tests indicates that fatigue failure is governed primarily by the maximum cyclic tensile strain. The compressive portion of the loading cycle has little effect on the number of cycles to failure. A new empirically derived equation is introduced to describe the influence of mean strain and strain amplitude on fatigue endurance. The results emphasize the critical role tensile strains may play in cement failure and loosening of total joint replacements.

    View details for Web of Science ID A1983RS35800012

    View details for PubMedID 6645450



    Rats in space for 18.5 days did not exhibit the normal gain in femoral bone strength of terrestrial controls. The strength deficit may have been caused by multiple factors including a diminished bone formation and an inhibition of the gain in tissue material strength. Centrifugation at 1g in space substantially enhanced bone strength, possibly by promoting more normal tissue maturation. Full recovery of bone strength was achieved 25 days after reentry.

    View details for Web of Science ID A1983RP84600014

    View details for PubMedID 6634715



    A Strain energy density (SED) criterion based on a fracture mechanics approach was used to assess the possible failure of acetabular bone cement after total hip replacement. Stress distributions in the cement at the bone-cement interface were calculated using two-dimensional finite element analyses. The results indicate that increasing the thickness of bone cement reduces the risk of cement fracture. The addition of a metal backing to the polyethylene cup and retention of the subchondral bone further reduces the risk of failure. The SED criterion was found to predict the same critical regions as zones of possible cement failure as the von Mises' criterion. Although either criterion can be used for predicting failure in this acetabular analysis both criteria are excessively conservative in predicting failure in regions where high principal compressive stresses are present. Further development of cement failure criteria are indicated.

    View details for Web of Science ID A1983RS35800003

    View details for PubMedID 6645441



    Two-dimensional finite element stress analyses were conducted of the acetabular region after total joint replacement. The effect of subchondral bone retention was evaluated for both conventional and metal-backed acetabular components. Stresses in the bone, cement and acetabular cup were significantly reduced when subchondral bone was retained for both component types. The results indicate that the most favorable stress conditions are created when a metal-backed acetabular component is implanted with subchondral bone retention.

    View details for Web of Science ID A1983QG68900004

    View details for PubMedID 6829279


    View details for Web of Science ID A1981LC40100007

    View details for PubMedID 7217116


    View details for Web of Science ID A1976BD22000005

    View details for PubMedID 1249078



    Cylindrical specimens of bovine subchondral trabecular bone were tested to uniaxial compressive strain levels of 75% to study energy absorption during pore collapse. Stress-strain curves were characterized by macroscopic yield at about 8% strain followed by a significant horizontal pore collapse regime. Energy absorption occurred largely in this postyield regime. Yield strength and energy absorption capacity were found to increase linearly with specimen apparent density. Microstructural analysis of the deformed specimens verfied that the mechanism for energy absorption was primarily fracture and buckling of trabeculae. The results suggest that during fracture, the collapse of trabecular bone (and the consequent absorption of energy) serves to attenuate stresses transmitted through the skeleton and thus protect vital structures such as the brain.

    View details for Web of Science ID A1976BZ90700007

    View details for PubMedID 947917


    View details for Web of Science ID A1976BM82100006

    View details for PubMedID 1262355

Conference Proceedings

  • Contributors to osteoporosis development Hernandez, C. J., Beaupre, G. S., Carter, D. R. SPRINGER LONDON LTD. 2003: 843-847
  • A theoretical analysis of the changes in basic multicellular unit activity at menopause Hernandez, C. J., Beaupre, G. S., Carter, D. R. ELSEVIER SCIENCE INC. 2003: 357-363


    Bone loss at menopause is an important contributor to the development of osteoporosis in women. Although alterations in bone remodeling are the implied process through which bone is lost at menopause, how menopause influences basic multicellular units (BMUs), the teams of cells that perform bone remodeling, is not completely clear. In this analysis we utilize a computer simulation of BMU activity to evaluate the changes that occur at menopause. Transient and maintained changes in both the rate of bone turnover (expressed as the BMU birthrate or origination frequency) and the focal bone balance (differences between the amount of bone formed and resorbed at each remodeling site) are considered. The magnitude of the change in BMU activity is determined parametrically through comparison to lumbar spine bone mineral density data present in the literature. We find that a change in bone turnover that is maintained after menopause, a transient change in focal bone balance at menopause, or a combination of the two is consistent with bone loss patterns seen clinically. Understanding the changes in BMU activity that occur at menopause could lead to improved strategies to treat and prevent postmenopausal osteoporosis.

    View details for DOI 10.1016/S8756-3282(03)00037-1

    View details for Web of Science ID 000182362900005

    View details for PubMedID 12689678

  • Long-term predictions of the therapeutic equivalence of daily and less than daily alendronate dosing Hernandez, C. J., Beaupre, G. S., Marcus, R., Carter, D. R. AMER SOC BONE & MINERAL RES. 2002: 1662-1666


    Less than daily alendronate dosing has been identified as an attractive alternative to daily dosing for patients and physicians. A recent 2-year study found bone mineral density (BMD) changes caused by weekly alendronate dosing therapeutically equivalent to that caused by daily dosing. There are no methods that can be used to predict how long therapeutic equivalence will be maintained after the first 2 years of treatment. In addition, it is unclear if dosing less frequently than weekly also might be therapeutically equivalent to daily dosing. In this study we use a computer simulation to develop predictions of the therapeutic equivalence of daily and less than daily dosing over time periods as long as a decade. The computer simulation uses a cell-based computer model of bone remodeling and a quantitative description of alendronate pharmacokinetics/pharmacodynamics (PK/PD). The analyses suggest that less than daily dosing regimens do not increase BMD as much as daily dosing. However, model predictions suggest that dosing as frequent as weekly still may be therapeutically equivalent to daily dosing over periods as long as 10 years. In addition, the simulations predict dosing less frequently than weekly may be therapeutically equivalent to daily dosing within the first year of treatment but may not be therapeutically equivalent after 10 years. Hypotheses based on these simulations may be useful for determining which dosing regimen may be most attractive for clinical trials.

    View details for Web of Science ID 000177616200013

    View details for PubMedID 12211437

  • Effects of shear stress on articular chondrocyte metabolism Smith, R. L., Trindade, M. C., Ikenoue, T., Mohtai, M., Das, P., Carter, D. R., Goodman, S. B., Schurman, D. J. IOS PRESS. 2000: 95-107


    The articular cartilage of diarthrodial joints experiences a variety of stresses, strains and pressures that result from normal activities of daily living. In normal cartilage, the extracellular matrix exists as a highly organized composite of specialized macromolecules that distributes loads at the bony ends. The chondrocyte response to mechanical loading is recognized as an integral component in the maintenance of articular cartilage matrix homeostasis. With inappropriate mechanical loading of the joint, as occurs with traumatic injury, ligament instability, bony malalignment or excessive weight bearing, the cartilage exhibits manifestations characteristic of osteoarthritis. Breakdown of cartilage in osteoarthritis involves degradation of the extracellular matrix macromolecules and decreased expression of chondrocyte proteins necessary for normal joint function. Osteoarthritic cartilage often exhibits increased amounts of type I collagen and synthesis of proteoglycans characteristic of immature cartilage. The shift in cartilage phenotype in response to altered load yields a matrix that fails to support normal joint function. Mathematical modeling and experimental studies in animal models confirm an association between altered loading of diarthrotic joints and arthritic changes. Both types of studies implicate shear forces as a critical component in the destructive profile. The severity of cartilage destruction in response to altered loads appears linked to expression of biological factors influencing matrix integrity and cellular metabolism. Determining how shear stress alters chondrocyte metabolism is fundamental to understanding how to limit matrix destruction and stimulate cartilage repair and regeneration. At present, the precise biochemical and molecular mechanisms by which shear forces alter chondrocyte metabolism from a normal to a degenerative phenotype remain unclear. The results presented here address the hypothesis that articular chondrocyte metabolism is modulated by direct effects of shear forces that act on the cell through mechanotransduction processes. The purpose of this work is to develop critical knowledge regarding the basic mechanisms by which mechanical loading modulates cartilage metabolism in health and disease. This presentation will describe the effects of using fluid induced shear stress as a model system for stimulation of articular chondrocytes in vitro. The fluid induced shear stress was applied using a cone viscometer system to stimulate all the cells uniformly under conditions of minimal turbulence. The experiments were carried using high-density primary monolayer cultures of normal and osteoarthritic human and normal bovine articular chondrocytes. The analysis of the cellular response included quantification of cytokine release, matrix metalloproteinase expression and activation of intracellular signaling pathways. The data presented here show that articular chondrocytes exhibit a dose- and time-dependent response to shear stress that results in the release of soluble mediators and extracellular matrix macromolecules. The data suggest that the chondrocyte response to mechanical stimulation contributes to the maintenance of articular cartilage homeostasis in vivo.

    View details for Web of Science ID 000088104400010

    View details for PubMedID 10912182

  • Mechanical factors in bone growth and development Carter, D. R., VANDERMEULEN, M. C., Beaupre, G. S. ELSEVIER SCIENCE INC. 1996: S5-S10


    Physical forces applied to connective tissues may cause significant changes in cell metabolism and gene expression. Theoretical investigations indicate that mechanical loading histories beginning very early in skeletal development may guide endochondral ossification patterns and the initial architectural construction of bones. Developmental patterns and structures of bones can be emulated using mathematical algorithms or "rules of construction" which relate developmental processes to tissue stress (or strain) histories. Skeletal forms and tissues are well-designed for their mechanical function primarily because their histomorphological construction has been guided by mechanical loading during growth and development. Construction rules of developmental mechanics can also be used to describe many of the histological and morphological adaptations of mature skeletal tissues to changes in customary physical activity. Over many generations, changes in the heritable genetic information occurs by mutation and genetic variability. The range of skeletal forms that are possible in evolution due to such variations, however, is constrained by the developmental rules of construction that reflect biophysical processes associated with the tissue mechanical loading.

    View details for Web of Science ID A1991HB54500002

    View details for PubMedID 1791178

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